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Sample records for hecke algebra diffeomorphism

  1. Hecke algebras with unequal parameters

    CERN Document Server

    Lusztig, G

    2003-01-01

    Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over p-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives rese...

  2. A trace formula for the Iwahori-Hecke algebra

    NARCIS (Netherlands)

    Opdam, E.M.

    1999-01-01

    The Iwahori-Hecke algebra has a canonicaltrace $\\tau$. The trace is the evaluation at the identity element in the usual interpretation of the Iwahori-Hecke algebra as a sub-algebra of the convolution algebra of a p-adic semi-simple group. The Iwahori-Hecke algebra contains an important commutative

  3. Representations of affine Hecke algebras

    CERN Document Server

    Xi, Nanhua

    1994-01-01

    Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest

  4. Blocks and families for cyclotomic Hecke algebras

    CERN Document Server

    Chlouveraki, Maria

    2009-01-01

    The definition of Rouquier for the families of characters introduced by Lusztig for Weyl groups in terms of blocks of the Hecke algebras has made possible the generalization of this notion to the case of complex reflection groups. The aim of this book is to study the blocks and to determine the families of characters for all cyclotomic Hecke algebras associated to complex reflection groups. This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory, and can also serve as an introduction to the Hecke algebras of complex reflection groups.

  5. Hecke symmetries and characteristic relations on reflection equation algebras

    International Nuclear Information System (INIS)

    Gurevich, D.I.; Pyatov, P.N.

    1996-01-01

    We discuss how properties of Hecke symmetry (i.e., Hecke type R-matrix) influence the algebraic structure of the corresponding Reflection Equation (RE) algebra. Analogues of the Newton relations and Cayley-Hamilton theorem for the matrix of generators of the RE algebra related to a finite rank even Hecke symmetry are derived. 10 refs

  6. Area-preserving diffeomorphisms and higher-spin algebras

    Energy Technology Data Exchange (ETDEWEB)

    Bergshoeff, E [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Blencowe, M P; Stelle, K S [Imperial Coll. of Science and Technology, London (UK). Blackett Lab.

    1990-03-01

    We show that there exists a one-parameter family of infinite-dimensional algebras that includes the bosonic d=3 Fradkin-Vasiliev higher-spin algebra and the non-Euclidean version of the algebra of area-preserving diffeomorphisms of the two-sphere S{sup 2} as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic space S{sup 1,1}, and can be rewritten as lim{sub Nyieldsinfinity} su(N,N). As an application of our results, we formulate a new d=2+1 massless higher-spin field theory as the gauge theory of the area-preserving diffeomorphisms of S{sup 1,1}. (orig.).

  7. Iwahori-Hecke algebras and Schur algebras of the symmetric group

    CERN Document Server

    Mathas, Andrew

    1999-01-01

    This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the q-Schur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers. The primary goal of the book is to classify the blocks and the simple modules of both algebras. The final chapter contains a survey of recent advances and open problems. The main results are proved by showing that the Iwahori-Hecke algebras and q-Schur algebras are cellular algebras (in the sense of Graham and Lehrer). This is proved by exhibiting natural bases of both algebras which are indexed by pairs of standard and semistandard tableaux respectively. Using the machinery of cellular algebras, which is developed in Chapter 2, this results in a clean and elegant classification of the irreducible representations of both algebras. The block theory is approached by first proving an analogue of the Jantzen sum formula for the q-Schur algebras. T...

  8. Extended Virasoro algebra and algebra of area preserving diffeomorphisms

    International Nuclear Information System (INIS)

    Arakelyan, T.A.

    1990-01-01

    The algebra of area preserving diffeomorphism plays an important role in the theory of relativistic membranes. It is pointed out that the relation between this algebra and the extended Virasoro algebra associated with the generalized Kac-Moody algebras G(T 2 ). The highest weight representation of these infinite-dimensional algebras as well as of their subalgebras is studied. 5 refs

  9. From affine Hecke algebras to boundary symmetries

    International Nuclear Information System (INIS)

    Doikou, Anastasia

    2005-01-01

    Motivated by earlier works we employ appropriate realizations of the affine Hecke algebra and we recover previously known non-diagonal solutions of the reflection equation for the U q (gl n -bar ) case. The corresponding N site spin chain with open boundary conditions is then constructed and boundary non-local charges associated to the non-diagonal solutions of the reflection equation are derived, as coproduct realizations of the reflection algebra. With the help of linear intertwining relations involving the aforementioned solutions of the reflection equation, the symmetry of the open spin chain with the corresponding boundary conditions is exhibited, being essentially a remnant of the U q (gl n -bar ) algebra. More specifically, we show that representations of certain boundary non-local charges commute with the generators of the affine Hecke algebra and with the local Hamiltonian of the open spin chain for a particular choice of boundary conditions. Furthermore, we are able to show that the transfer matrix of the open spin chain commutes with a certain number of boundary non-local charges, depending on the choice of boundary conditions

  10. Markov trace on the Yokonuma-Hecke algebra

    International Nuclear Information System (INIS)

    Juyumaya, J.

    2002-11-01

    The objective of this note is to prove that there exists a Markov trace on the Yokonuma-Hecke algebra. A motivation to define a Markov trace is to get polynomial invariants for knots in the sense of Jones construction. (author)

  11. C*-algebras of holonomy-diffeomorphisms and quantum gravity: I

    International Nuclear Information System (INIS)

    Aastrup, Johannes; Grimstrup, Jesper Møller

    2013-01-01

    A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a quantized Dirac-type operator, the two capturing the kinematics of quantum gravity formulated in terms of Ashtekar variables. We prove that the separable part of the spectrum of the algebra is contained in the space of measurable connections modulo gauge transformations and we give limitations to the non-separable part. The construction of the Dirac-type operator—and thus the application of noncommutative geometry—is motivated by the requirement of diffeomorphism invariance. We conjecture that a semi-finite spectral triple, which is invariant under volume-preserving diffeomorphisms, arises from a GNS construction of a semi-classical state. Key elements of quantum field theory emerge from the construction in a semi-classical limit, as does an almost commutative algebra. Finally, we note that the spectrum of loop quantum gravity emerges from a discretization of our construction. Certain convergence issues are left unresolved. This paper is the first of two where the second paper [1] is concerned with mathematical details and proofs concerning the spectrum of the holonomy-diffeomorphism algebra. (paper)

  12. Large chiral diffeomorphisms on Riemann surfaces and W-algebras

    International Nuclear Information System (INIS)

    Bandelloni, G.; Lazzarini, S.

    2006-01-01

    The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a Becchi-Rouet-Stora (BRS) formulation (for a given order of truncation) leading to a more algebraic setup. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so-called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between Korteweg-de Vries (KdV) flows and W-diffeomorphims

  13. Matrix units and Schur elements for the degenerate cyclotomic Hecke algebras

    OpenAIRE

    Zhao, Deke

    2011-01-01

    The paper uses the cellular basis of the (semi-simple) degenerate cyclotomic Hecke algebras to investigate these algebras exhaustively. As a consequence, we describe explicitly the "Young's seminormal form" and a orthogonal bases for Specht modules and determine explicitly the closed formula for the natural bilinear form on Specht modules and Schur elements for the degenerate cyclotomic Hekce algebras.

  14. Property (RD) for Hecke Pairs

    International Nuclear Information System (INIS)

    Shirbisheh, Vahid

    2012-01-01

    As the first step towards developing noncommutative geometry over Hecke C ∗ -algebras, we study property (RD) (Rapid Decay) for Hecke pairs. When the subgroup H in a Hecke pair (G, H) is finite, we show that the Hecke pair (G, H) has (RD) if and only if G has (RD). This provides us with a family of examples of Hecke pairs with property (RD). We also adapt Paul Jolissant’s works in Jolissaint (J K-Theory 2:723–735, 1989; Trans Amer Math Soc 317(1):167–196, 1990) to the setting of Hecke C ∗ -algebras and show that when a Hecke pair (G, H) has property (RD), the algebra of rapidly decreasing functions on the set of double cosets is closed under holomorphic functional calculus of the associated (reduced) Hecke C ∗ -algebra. Hence they have the same K 0 -groups.

  15. Eisenstein Hecke algebras and Iwasawa theory

    Science.gov (United States)

    Wake, Preston

    We show that if an Eisenstein component of the p-adic Hecke algebra associated to modular forms is Gorenstein, then it is necessary that the plus-part of a certain ideal class group is trivial. We also show that this condition is sufficient whenever a conjecture of Sharifi holds. We also formulate a weaker Gorenstein property, and show that this weak Gorenstein property holds if and only if a weak form of Sharifi's conjecture and a weak form of Greenberg's conjecture hold.

  16. Hecke algebraic properties of dynamical R-matrices. Application to related quantum matrix algebras

    International Nuclear Information System (INIS)

    Khadzhiivanov, L.K.; Todorov, I.T.; Isaev, A.P.; Pyatov, P.N.; Ogievetskij, O.V.

    1998-01-01

    The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines an R-matrix R cap (p), where p stands for a set of mutually commuting variables. A family of SL (n)-type solutions of this equation provides a new realization of the Hecke algebra. We define quantum antisymmetrizers, introduce the notion of quantum determinant and compute the inverse quantum matrix for matrix algebras of the type R cap (p) a 1 a 2 = a 1 a 2 R cap. It is pointed out that such a quantum matrix algebra arises in the operator realization of the chiral zero modes of the WZNW model

  17. Spherical Hecke algebra in the Nekrasov-Shatashvili limit

    Energy Technology Data Exchange (ETDEWEB)

    Bourgine, Jean-Emile [Asia Pacific Center for Theoretical Physics (APCTP),Pohang, Gyeongbuk 790-784 (Korea, Republic of)

    2015-01-21

    The Spherical Hecke central (SHc) algebra has been shown to act on the Nekrasov instanton partition functions of N=2 gauge theories. Its presence accounts for both integrability and AGT correspondence. On the other hand, a specific limit of the Omega background, introduced by Nekrasov and Shatashvili (NS), leads to the appearance of TBA and Bethe like equations. To unify these two points of view, we study the NS limit of the SHc algebra. We provide an expression of the instanton partition function in terms of Bethe roots, and define a set of operators that generates infinitesimal variations of the roots. These operators obey the commutation relations defining the SHc algebra at first order in the equivariant parameter ϵ{sub 2}. Furthermore, their action on the bifundamental contributions reproduces the Kanno-Matsuo-Zhang transformation. We also discuss the connections with the Mayer cluster expansion approach that leads to TBA-like equations.

  18. New phases of D≥2 current and diffeomorphism algebras in particle physics

    International Nuclear Information System (INIS)

    Tze, Chia-Hsiung.

    1990-09-01

    We survey some global results and open issues of current algebras and their canonical field theoretical realization in D ≥ 2 dimensional spacetime. We assess the status of the representation theory of their generalized Kac-Moody and diffeomorphism algebras. Particular emphasis is put on higher dimensional analogs of fermi-bose correspondence, complex analyticity and the phase entanglements of anyonic solitons with exotic spin and statistics. 101 refs

  19. Group characters, symmetric functions, and the Hecke algebra

    CERN Document Server

    Goldschmidt, David M

    1993-01-01

    Directed at graduate students and mathematicians, this book covers an unusual set of interrelated topics, presenting a self-contained exposition of the algebra behind the Jones polynomial along with various excursions into related areas. The book is made up of lecture notes from a course taught by Goldschmidt at the University of California at Berkeley in 1989. The course was organized in three parts. Part I covers, among other things, Burnside's Theorem that groups of order p^aq^b are solvable, Frobenius' Theorem on the existence of Frobenius kernels, and Brauer's characterization of characters. Part II covers the classical character theory of the symmetric group and includes an algorithm for computing the character table of S^n ; a construction of the Specht modules; the "determinant form" for the irreducible characters; the hook-length formula of Frame, Robinson, and Thrall; and the Murnaghan-Nakayama formula. Part III covers the ordinary representation theory of the Hecke algebra, the construction of the ...

  20. R-matrix arising from affine Hecke algebras and its application to Macdonald's difference operators

    International Nuclear Information System (INIS)

    Kato, Shinichi

    1994-01-01

    We shall give a certain trigonometric R-matrix associated with each root system by using affine Hecke algebras. From this R-matrix, we derive a quantum Knizhnik-Zamolodchikov equation after Cherednik, and show that the solutions of this KZ equation yield eigenfunctions of Macdonald's difference operators. (orig.)

  1. New phases of D ge 2 current and diffeomorphism algebras in particle physics

    Energy Technology Data Exchange (ETDEWEB)

    Tze, Chia-Hsiung.

    1990-09-01

    We survey some global results and open issues of current algebras and their canonical field theoretical realization in D {ge} 2 dimensional spacetime. We assess the status of the representation theory of their generalized Kac-Moody and diffeomorphism algebras. Particular emphasis is put on higher dimensional analogs of fermi-bose correspondence, complex analyticity and the phase entanglements of anyonic solitons with exotic spin and statistics. 101 refs.

  2. Two-rowed Hecke algebra representations at roots of unity

    International Nuclear Information System (INIS)

    Welsh, T.A.

    1996-01-01

    The explicit construction of irreducible representations of the Hecke algebra H n (q) of type A n-1 was studied for the non-generic case where q is a root of unity. The approach is via the Specht modules of H n (q) which are irreducible in the generic case and possess a natural basis indexed by Young tableaux. The general framework in which the non-generic H n (q)-modules are to be constructed is set up and, in particular, the full set of modules corresponding to two-part partitions is described. Many examples are given. 12 refs

  3. Nekrasov and Argyres–Douglas theories in spherical Hecke algebra representation

    Energy Technology Data Exchange (ETDEWEB)

    Rim, Chaiho, E-mail: rimpine@sogang.ac.kr; Zhang, Hong, E-mail: kilar@itp.ac.cn

    2017-06-15

    AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate representation, q being the instanton expansion parameter. Based on AFLT basis together with intertwiners we construct gauge conformal state and demonstrate its equivalence to the Liouville conformal state, with careful attention to the proper scaling behavior of the state. Using the colliding limit of regular states, we obtain the formal expression of irregular conformal states corresponding to Argyres–Douglas theory, which involves summation of functions over Young diagrams.

  4. Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation

    Science.gov (United States)

    Rim, Chaiho; Zhang, Hong

    2017-06-01

    AGT conjecture connects Nekrasov instanton partition function of 4D quiver gauge theory with 2D Liouville conformal blocks. We re-investigate this connection using the central extension of spherical Hecke algebra in q-coordinate representation, q being the instanton expansion parameter. Based on AFLT basis together with intertwiners we construct gauge conformal state and demonstrate its equivalence to the Liouville conformal state, with careful attention to the proper scaling behavior of the state. Using the colliding limit of regular states, we obtain the formal expression of irregular conformal states corresponding to Argyres-Douglas theory, which involves summation of functions over Young diagrams.

  5. Current algebras, measures quasi-invariant under diffeomorphism groups, and infinite quantum systems with accumulation points

    Science.gov (United States)

    Sakuraba, Takao

    The approach to quantum physics via current algebra and unitary representations of the diffeomorphism group is established. This thesis studies possible infinite Bose gas systems using this approach. Systems of locally finite configurations and systems of configurations with accumulation points are considered, with the main emphasis on the latter. In Chapter 2, canonical quantization, quantization via current algebra and unitary representations of the diffeomorphism group are reviewed. In Chapter 3, a new definition of the space of configurations is proposed and an axiom for general configuration spaces is abstracted. Various subsets of the configuration space, including those specifying the number of points in a Borel set and those specifying the number of accumulation points in a Borel set are proved to be measurable using this axiom. In Chapter 4, known results on the space of locally finite configurations and Poisson measure are reviewed in the light of the approach developed in Chapter 3, including the approach to current algebra in the Poisson space by Albeverio, Kondratiev, and Rockner. Goldin and Moschella considered unitary representations of the group of diffeomorphisms of the line based on self-similar random processes, which may describe infinite quantum gas systems with clusters. In Chapter 5, the Goldin-Moschella theory is developed further. Their construction of measures quasi-invariant under diffeomorphisms is reviewed, and a rigorous proof of their conjectures is given. It is proved that their measures with distinct correlation parameters are mutually singular. A quasi-invariant measure constructed by Ismagilov on the space of configurations with accumulation points on the circle is proved to be singular with respect to the Goldin-Moschella measures. Finally a generalization of the Goldin-Moschella measures to the higher-dimensional case is studied, where the notion of covariance matrix and the notion of condition number play important roles. A

  6. On nonlinear equations associated with Lie algebras of diffeomorphism groups of two-dimensional manifolds

    International Nuclear Information System (INIS)

    Kashaev, R.M.; Savel'ev, M.V.; Savel'eva, S.A.

    1990-01-01

    Nonlinear equations associated through a zero curvature type representation with Lie algebras S 0 Diff T 2 and of infinitesimal diffeomorphisms of (S 1 ) 2 , and also with a new infinite-dimensional Lie algebras. In particular, the general solution (in the sense of the Goursat problem) of the heavently equation which describes self-dual Einstein spaces with one rotational Killing symmetry is discussed, as well as the solutions to a generalized equation. The paper is supplied with Appendix containing the definition of the continuum graded Lie algebras and the general construction of the nonlinear equations associated with them. 11 refs

  7. Quasi-coherent Hecke category and Demazure descent

    DEFF Research Database (Denmark)

    Arkhipov, Sergey; Kanstrup, Tina

    2015-01-01

    Let G be a reductive algebraic group with a Borel subgroup B. We define the quasi-coherent Hecke category for the pair (G,B). For any regular Noetherian G- scheme X we construct a monoidal action of the Hecke category on the derived category of B-equivariant quasi-coherent sheaves on X. Using the...

  8. A Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank

    Science.gov (United States)

    Fu, Yuchen; Shelley-Abrahamson, Seth

    2016-06-01

    We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for U_q(sl_N). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld-Kohno theorem for Knizhnik-Zamolodchikov differential equations, we prove that the explicit representations we produce correspond to Montarani's representations under a monodromy functor introduced by Etingof, Gan, and Oblomkov.

  9. Space-Time Diffeomorphisms in Noncommutative Gauge Theories

    Directory of Open Access Journals (Sweden)

    L. Román Juarez

    2008-07-01

    Full Text Available In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007, 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985, 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987, 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.

  10. Diffeomorphism-type symmetries of the self-dual Yang-Mills equations

    International Nuclear Information System (INIS)

    Ivanova, T.A.

    1998-01-01

    The infinite-dimensional algebra of diffeomorphism-type symmetries of the self-dual Yang-Mills equations is described as the algebra of 0-cochains with values in a sheaf of germs of holomorphic sections of the (1,0) tangent bundle over the twistor space. It is shown that the extended conformal symmetries are obtained as particular cases of the aforementioned algebra

  11. Extended Kac-Moody algebras and applications

    International Nuclear Information System (INIS)

    Ragoucy, E.; Sorba, P.

    1991-04-01

    The notion of a Kac-Moody algebra defined on the S 1 circle is extended to super Kac-Moody algebras defined on MxG N , M being a smooth closed compact manifold of dimension greater than one, and G N the Grassman algebra with N generators. All the central extensions of these algebras are computed. Then, for each such algebra the derivation algebra constructed from the MxG N diffeomorphism is determined. The twists of such super Kac-Moody algebras as well as the generalization to non-compact surfaces are partially studied. Finally, the general construction is applied to the study of conformal and superconformal algebras, as well as area-preserving diffeomorphisms algebra and its supersymmetric extension. (author) 65 refs

  12. Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space

    International Nuclear Information System (INIS)

    Pons, Josep M

    2003-01-01

    Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms being projectable to phase space, for generally covariant theories. This main result throws new light on the old fact that the algebra of gauge generators in the phase space of general relativity, or other generally covariant theories, only closes as a soft algebra and not as a Lie algebra. The deep relationship between these two issues is clarified. In particular, we see that the second one may be understood as a side effect of the procedure to solve the first. It is explicitly shown how the adoption of specific metric-dependent diffeomorphisms, as a way to achieve projectability, causes the algebra of gauge generators (constraints) in phase space not to be a Lie algebra -with structure constants - but a soft algebra - with structure functions

  13. Diffeomorphisms Holder conjugate to Anosov diffeomorphisms

    OpenAIRE

    Gogolev, Andrey

    2008-01-01

    We show by means of a counterexample that a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is not necessarily Anosov. The counterexample can bear higher smoothness up to $C^3$. Also we include a result from the 2006 Ph.D. thesis of T. Fisher: a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is Anosov itself provided that Holder exponents of the conjugacy and its inverse are sufficiently large.

  14. A combinatorial approach to diffeomorphism invariant quantum gauge theories

    International Nuclear Information System (INIS)

    Zapata, J.A.

    1997-01-01

    Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical states are gauge and diffeomorphism invariant distributions on the space of functions of the holonomies of the edges of a certain family of graphs. Then a family of graphs embedded in the space manifold (satisfying certain properties) induces a representation of the algebra of physical observables. We construct a quantum model from the set of piecewise linear graphs on a piecewise linear manifold, and another manifestly combinatorial model from graphs defined on a sequence of increasingly refined simplicial complexes. Even though the two models are different at the kinematical level, they provide unitarily equivalent representations of the algebra of physical observables in separable Hilbert spaces of physical states (their s-knot basis is countable). Hence, the combinatorial framework is compatible with the usual interpretation of quantum field theory. copyright 1997 American Institute of Physics

  15. Chern-Simons theories of symplectic super-diffeomorphisms

    International Nuclear Information System (INIS)

    Sezgin, E.; Sokatchev, E.

    1989-04-01

    We discuss the symplectic diffeomorphisms of a class of supermanifolds and the structure of the underlying infinite dimensional superalgebras. We construct a Chern-Simons (CS) gauge theory in 2+1 dimensions for these algebras. There exists a finite dimensional supersymmetric truncation which is the (2 n -1)-dimensional Hamiltonian superalgebra H-tilde(n). With a central charge added, it is a superalgebra, C(n), associated with a Clifford algebra. We find an embedding of d=3, N=2 anti-de Sitter superalgebra OSp(2|2)+OSp(2|2) in C(4), and construct a CS action for its infinite dimensional extension. We also discuss the construction of a CS action for the infinite dimensional extension of the d=3, N=2 superconformal algebra OSp(2,4). (author). 18 refs

  16. New examples of continuum graded Lie algebras

    International Nuclear Information System (INIS)

    Savel'ev, M.V.

    1989-01-01

    Several new examples of continuum graded Lie algebras which provide an additional elucidation of these algebras are given. Here, in particular, the Kac-Moody algebras, the algebra S 0 Diff T 2 of infinitesimal area-preserving diffeomorphisms of the torus T 2 , the Fairlie, Fletcher and Zachos sine-algebras, etc., are described as special cases of the cross product Lie algebras. 8 refs

  17. Lorentz-diffeomorphism quasi-local conserved charges and Virasoro algebra in Chern–Simons-like theories of gravity

    Directory of Open Access Journals (Sweden)

    M.R. Setare

    2016-08-01

    Full Text Available The Chern–Simons-like theories of gravity (CSLTG are formulated at first order formalism. In this formalism, the derivation of the entropy of a black hole on bifurcation surface, as a quasi-local conserved charge is problematic. In this paper we overcome these problems by considering the concept of total variation and the Lorentz–Lie derivative. We firstly find an expression for the ADT conserved current in the context of the CSLTG which is based on the concept of the Killing vector fields. Then, we generalize it to be conserved for all diffeomorphism generators. Thus, we can extract an off-shell conserved charge for any vector field which generates a diffeomorphism. The formalism presented here is based on the concept of quasi-local conserved charges which are off-shell. The charges can be calculated on any codimension two space-like surface surrounding a black hole and the results are independent of the chosen surface. By using the off-shell quasi-local conserved charge, we investigate the Virasoro algebra and find a formula to calculate the central extension term. We apply the formalism to the BTZ black hole solution in the context of the Einstein gravity and the Generalized massive gravity, then we find the eigenvalues of their Virasoro generators as well as the corresponding central charges. Eventually, we calculate the entropy of the BTZ black hole by the Cardy formula and we show that the result exactly matches the one obtained by the concept of the off-shell conserved charges.

  18. Representations of quantum algebras and combinatorics of Young tableaux

    CERN Document Server

    Ariki, Susumu

    2002-01-01

    Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and to apply the theory to representations of Hecke algebras. The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type A_{r-1}^{(1)} as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be the combinatorics of Young tableaux. The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type. The book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the stu...

  19. The Fuzzy analogy of chiral diffeomorphisms in higher dimensional quantum field theories

    International Nuclear Information System (INIS)

    Fassarella, Lucio; Schroer, Bert

    2001-06-01

    Our observation that the chiral diffeomorphisms allow an interpretation as modular groups of local operator algebras in the sense of Tomita and takesaki allows us to conclude that the higher deimensional generalizations are certain infinite dimensional groups which act in a 'fuzzy' way on the operator algebras of local quantum physics. These actions do not require any spacetime noncommutativity and are in complete harmony with causality and localization principles. The use of an appropriately defined isomorphism reprocesses these fuzzy actions into partially geometric actions on the holographic image and in this way tightens the relation with chiral structures and makes recent attempts to explain the required universal structure of a would be quantum Bekenstein law in terms of Virasoro algebra structures more palatable. (author)

  20. Morphometric brain characterization of refractory obsessive-compulsive disorder: diffeomorphic anatomic registration using exponentiated Lie algebra.

    Science.gov (United States)

    Tang, Wanjie; Li, Bin; Huang, Xiaoqi; Jiang, Xiaoyu; Li, Fei; Wang, Lijuan; Chen, Taolin; Wang, Jinhui; Gong, Qiyong; Yang, Yanchun

    2013-10-01

    Few studies have used neuroimaging to characterize treatment-refractory obsessive-compulsive disorder (OCD). This study sought to explore gray matter structure in patients with treatment-refractory OCD and compare it with that of healthy controls. A total of 18 subjects with treatment-refractory OCD and 26 healthy volunteers were analyzed by MRI using a 3.0-T scanner and voxel-based morphometry (VBM). Diffeomorphic anatomical registration using exponentiated Lie algebra (DARTEL) was used to identify structural changes in gray matter associated with treatment-refractory OCD. A partial correlation model was used to analyze whether morphometric changes were associated with Yale-Brown Obsessive-Compulsive Scale scores and illness duration. Gray matter volume did not differ significantly between the two groups. Treatment-refractory OCD patients showed significantly lower gray matter density than healthy subjects in the left posterior cingulate cortex (PCC) and mediodorsal thalamus (MD) and significantly higher gray matter density in the left dorsal striatum (putamen). These changes did not correlate with symptom severity or illness duration. Our findings provide new evidence of deficits in gray matter density in treatment-refractory OCD patients. These patients may show characteristic density abnormalities in the left PCC, MD and dorsal striatum (putamen), which should be verified in longitudinal studies. © 2013. Published by Elsevier Inc. All rights reserved.

  1. Infinite dimension algebra and conformal symmetry

    International Nuclear Information System (INIS)

    Ragoucy-Aubezon, E.

    1991-04-01

    A generalisation of Kac-Moody algebras (current algebras defined on a circle) to algebras defined on a compact supermanifold of any dimension and with any number of supersymmetries is presented. For such a purpose, we compute all the central extensions of loop algebras defined on this supermanifold, i.e. all the cohomology classes of these loop algebras. Then, we try to extend the relation (i.e. semi-direct sum) that exists between the two dimensional conformal algebras (called Virasoro algebra) and the usual Kac-Moody algebras, by considering the derivation algebra of our extended Kac-Moody algebras. The case of superconformal algebras (used in superstrings theories) is treated, as well as the cases of area-preserving diffeomorphisms (used in membranes theories), and Krichever-Novikov algebras (used for interacting strings). Finally, we present some generalizations of the Sugawara construction to the cases of extended Kac-Moody algebras, and Kac-Moody of superalgebras. These constructions allow us to get new realizations of the Virasoro, and Ramond, Neveu-Schwarz algebras

  2. Centrally extended symmetry algebra of asymptotically Goedel spacetimes

    International Nuclear Information System (INIS)

    Compere, Geoffrey; Detournay, Stephane

    2007-01-01

    We define an asymptotic symmetry algebra for three-dimensional Goedel spacetimes supported by a gauge field which turns out to be the semi-direct sum of the diffeomorphisms on the circle with two loop algebras. A class of fields admitting this asymptotic symmetry algebra and leading to well-defined conserved charges is found. The covariant Poisson bracket of the conserved charges is then shown to be centrally extended to the semi-direct sum of a Virasoro algebra and two affine algebras. The subsequent analysis of three-dimensional Goedel black holes indicates that the Virasoro central charge is negative

  3. Voxel-based morphometric analysis in hypothyroidism using diffeomorphic anatomic registration via an exponentiated lie algebra algorithm approach.

    Science.gov (United States)

    Singh, S; Modi, S; Bagga, D; Kaur, P; Shankar, L R; Khushu, S

    2013-03-01

    The present study aimed to investigate whether brain morphological differences exist between adult hypothyroid subjects and age-matched controls using voxel-based morphometry (VBM) with diffeomorphic anatomic registration via an exponentiated lie algebra algorithm (DARTEL) approach. High-resolution structural magnetic resonance images were taken in ten healthy controls and ten hypothyroid subjects. The analysis was conducted using statistical parametric mapping. The VBM study revealed a reduction in grey matter volume in the left postcentral gyrus and cerebellum of hypothyroid subjects compared to controls. A significant reduction in white matter volume was also found in the cerebellum, right inferior and middle frontal gyrus, right precentral gyrus, right inferior occipital gyrus and right temporal gyrus of hypothyroid patients compared to healthy controls. Moreover, no meaningful cluster for greater grey or white matter volume was obtained in hypothyroid subjects compared to controls. Our study is the first VBM study of hypothyroidism in an adult population and suggests that, compared to controls, this disorder is associated with differences in brain morphology in areas corresponding to known functional deficits in attention, language, motor speed, visuospatial processing and memory in hypothyroidism. © 2012 British Society for Neuroendocrinology.

  4. Differential calculi on quantum vector spaces with Hecke-type relations

    International Nuclear Information System (INIS)

    Baez, J.C.

    1991-01-01

    From a vector space V equipped with a Yang-Baxter operator R one may form the r-symmetric algebra S R V=TV/ , which is a quantum vector space in the sense of Manin, and the associated quantum matrix algebra M R V=T(End(V))/ -1 >. In the case when R satisfies a Hecke-type identity R 2 =(1-q)R+q, we construct a differential calculus Ω R V for S R V which agrees with that constructed by Pusz, Woronowicz, Wess, and Zumino when R is essentially the R-matrix of GL q (n). Elements of Ω R V may be regarded as differential forms on the quantum vector space S R V. We show that Ω R V is M R V-covariant in the sense that there is a coaction Φ * :Ω R V→M R VxΩ R V with Φ * d=(1xd)Φ * extending the natural coaction Φ:S R V→M R VxS R V. (orig.)

  5. On the q-deformation of certain infinite dimensional Lie algebras

    International Nuclear Information System (INIS)

    El Kinani, E.H.; Zakkari, M.

    1995-07-01

    A representation of the q-deformed centreless Virasoro algebra in terms of the Gauss derivatives D x and D y on the quantum plane C q [x,y] is given. Moreover, we obtain the deformed version of the algebra of the area-preserving diffeomorphisms of the torus T 2 . In the end, the correspondence between Psd(q,p,r) and the a-bar ∞ algebra is pointed out. (author). 11 refs

  6. White matter abnormalities in young males with antisocial personality disorder Evidence from voxel-based morphometry-diffeomorphic anatomical registration using exponentiated lie algebra analysis

    Institute of Scientific and Technical Information of China (English)

    Daxing Wu; Ying Zhao; Jian Liao; Huifang Yin; Wei Wang

    2011-01-01

    Voxel-based morphometry-diffeomorphic anatomical registration using exponentiated lie algebra analysis was used to investigate the structural characteristics of white matter in young males with antisocial personality disorder (APD) and healthy controls without APD. The results revealed that APD subjects, relative to healthy subjects, exhibited increased white matter volume in the bilateral prefrontal lobe, right insula, precentral gyrus, bilateral superior temporal gyrus, right postcentral gyrus, right inferior parietal lobule, right precuneus, right middle occipital lobe, right parahippocampal gyrus and bilateral cingulate, and decreased volume in the middle temporal cortex and right cerebellum. The white matter volume in the medial frontal gyrus was significantly correlated with antisocial type scores on the Personality Diagnostic Questionnaire in APD subjects. These experimental findings indicate that white matter abnormalities in several brain areas may contribute to antisocial behaviors in APD subjects.

  7. Torsional Newton-Cartan geometry and the Schrodinger algebra

    NARCIS (Netherlands)

    Bergshoeff, Eric A.; Hartong, Jelle; Rosseel, Jan

    2015-01-01

    We show that by gauging the Schrodinger algebra with critical exponent z and imposing suitable curvature constraints, that make diffeomorphisms equivalent to time and space translations, one obtains a geometric structure known as (twistless) torsional Newton-Cartan geometry (TTNC). This is a version

  8. w∞ algebras, conformal mechanics and black holes

    Science.gov (United States)

    Cacciatori, Sergio; Klemm, Dietmar; Zanon, Daniela

    2000-04-01

    We discuss BPS solitons in gauged icons/Journals/Common/calN" ALT="calN" ALIGN="TOP"/> = 2, D = 4 supergravity. The solitons represent extremal black holes interpolating between different vacua of anti-de Sitter spaces. The isometry superalgebras are determined and the motion of a superparticle in the extremal black hole background is studied and confronted with superconformal mechanics. We show that the Virasoro symmetry of conformal mechanics, which describes the dynamics of the superparticle near the horizon of the extremal black hole under consideration, extends to a symmetry under the wicons/Journals/Common/infty" ALT="infty" ALIGN="MIDDLE"/> algebra of area-preserving diffeomorphisms. We find that a Virasoro subalgebra of wicons/Journals/Common/infty" ALT="infty" ALIGN="MIDDLE"/> can be associated with the Virasoro algebra of the asymptotic symmetries of AdS 2 . In this way spacetime diffeomorphisms of AdS 2 translate into diffeomorphisms in phase space: our system offers an explicit realization of the AdS 2 /CFT 1 correspondence. Using the dimensionally reduced action, the central charge is computed. Finally, we also present generalizations of superconformal mechanics which are invariant under icons/Journals/Common/calN" ALT="calN" ALIGN="TOP"/> = 1 and icons/Journals/Common/calN" ALT="calN" ALIGN="TOP"/> = 2 superextensions of wicons/Journals/Common/infty" ALT="infty" ALIGN="MIDDLE"/> .

  9. Computing Diffeomorphic Paths for Large Motion Interpolation.

    Science.gov (United States)

    Seo, Dohyung; Jeffrey, Ho; Vemuri, Baba C

    2013-06-01

    In this paper, we introduce a novel framework for computing a path of diffeomorphisms between a pair of input diffeomorphisms. Direct computation of a geodesic path on the space of diffeomorphisms Diff (Ω) is difficult, and it can be attributed mainly to the infinite dimensionality of Diff (Ω). Our proposed framework, to some degree, bypasses this difficulty using the quotient map of Diff (Ω) to the quotient space Diff ( M )/ Diff ( M ) μ obtained by quotienting out the subgroup of volume-preserving diffeomorphisms Diff ( M ) μ . This quotient space was recently identified as the unit sphere in a Hilbert space in mathematics literature, a space with well-known geometric properties. Our framework leverages this recent result by computing the diffeomorphic path in two stages. First, we project the given diffeomorphism pair onto this sphere and then compute the geodesic path between these projected points. Second, we lift the geodesic on the sphere back to the space of diffeomerphisms, by solving a quadratic programming problem with bilinear constraints using the augmented Lagrangian technique with penalty terms. In this way, we can estimate the path of diffeomorphisms, first, staying in the space of diffeomorphisms, and second, preserving shapes/volumes in the deformed images along the path as much as possible. We have applied our framework to interpolate intermediate frames of frame-sub-sampled video sequences. In the reported experiments, our approach compares favorably with the popular Large Deformation Diffeomorphic Metric Mapping framework (LDDMM).

  10. Current algebras and many-body physics

    International Nuclear Information System (INIS)

    Albertin, U.K.

    1989-01-01

    Several applications of current algebras in many body physics are examined. The first is the interacting Bose gas in three dimensions. Theories for phonons, vortices and rotons are all described within the current algebra formalism. Next the one dimensional electron gas is examined within the approximation of linear dispersion so that relativistic current algebra techniques may be used. The relation with Thirring strings and compactified boson models is examined, and points of enhanced symmetry in the compactified boson models are shown to lie on phase transition lines for the electron gas. Finally, mathematical aspects of the current algebra are studied. The theory of induced representations of the diffeomorphism group are used to describe the Aharanov-Bohm effect, the thermodynamics of the Bose gas, and the Bose gas in the presence of vortex filaments

  11. On diffeomorphism invariance for lattice theories

    International Nuclear Information System (INIS)

    Corichi, A.; Zapata, J.

    1997-01-01

    We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices one automatically takes care of the diffeomorphism constraint in the quantum theory. We use two systems in order to show that imposing the diffeomorphism constraint is imperative to obtain a physically acceptable quantum theory. First, we consider 2+1 gravity where an exact lattice formulation is available. Next, general theories of connections for compact gauge groups are treated, where the quantum theories are known - for both the continuum and the lattice - and can be compared. (orig.)

  12. Diffeomorphic Statistical Deformation Models

    DEFF Research Database (Denmark)

    Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus

    2007-01-01

    In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al....... The modifications ensure that no boundary restriction has to be enforced on the parameter space to prevent folds or tears in the deformation field. For straightforward statistical analysis, principal component analysis and sparse methods, we assume that the parameters for a class of deformations lie on a linear...... with ground truth in form of manual expert annotations, and compared to Cootes's model. We anticipate applications in unconstrained diffeomorphic synthesis of images, e.g. for tracking, segmentation, registration or classification purposes....

  13. Consistency conditions and representations of a q-deformed Virasoro algebra

    International Nuclear Information System (INIS)

    Polychronakos, A.P.

    1990-01-01

    We derive deformations of the Virasoro algebra in terms of ''diffeomorphisms'' of functions on a discretized circle. The Curtright-Zachos deformation is recovered in one case, for deformation parameter a root of unity. Consistency conditions are then derived for this algebra by introducing the so-called ''braid-Jacobi'' identities. All the representations are subsequently found through use of these identities. Further, it is shown that no nontrivial central term can be incorporated, since it clashes with the consistency conditions. Finally, an alternative deformation is derived which generalizes the Drinfeld deformation of the Su(1,1) subgroup to the full algebra. 16 refs

  14. Atomic disintegrations for partially hyperbolic diffeomorphisms

    NARCIS (Netherlands)

    Homburg, Ale Jan

    2017-01-01

    Shub and Wilkinson and Ruelle and Wilkinson studied a class of volume preserving diffeomorphisms on the three dimensional torus that are stably ergodic. The diffeomorphisms are partially hyperbolic and admit an invariant central foliation of circles. The foliation is not absolutely continuous; in

  15. Current algebra, statistical mechanics and quantum models

    Science.gov (United States)

    Vilela Mendes, R.

    2017-11-01

    Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.

  16. Taking off the square root of Nambu-Goto action and obtaining Filippov-Lie algebra gauge theory action

    International Nuclear Information System (INIS)

    Park, Jeong-Hyuck; Sochichiu, Corneliu

    2009-01-01

    We propose a novel prescription to take off the square root of the Nambu-Goto action for a p-brane, which generalizes the Brink-Di Vecchia-Howe-Tucker, also known as the Polyakov method. With an arbitrary decomposition, d+n=p+1, our resulting action is a modified d-dimensional Polyakov action, which is gauged and possesses a Nambu n-bracket squared potential. We first spell out how the (p+1)-dimensional diffeomorphism is realized in the lower dimensional action. Then we discuss a possible gauge fixing of it to a direct product of d-dimensional diffeomorphism and n-dimensional volume preserving diffeomorphism. We show that the latter naturally leads to a novel Filippov-Lie n-algebra based gauge theory action in d dimensions. (orig.)

  17. Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra provides reduced effect of scanner for cortex volumetry with atlas-based method in healthy subjects.

    Science.gov (United States)

    Goto, Masami; Abe, Osamu; Aoki, Shigeki; Hayashi, Naoto; Miyati, Tosiaki; Takao, Hidemasa; Iwatsubo, Takeshi; Yamashita, Fumio; Matsuda, Hiroshi; Mori, Harushi; Kunimatsu, Akira; Ino, Kenji; Yano, Keiichi; Ohtomo, Kuni

    2013-07-01

    This study aimed to investigate whether the effect of scanner for cortex volumetry with atlas-based method is reduced using Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL) normalization compared with standard normalization. Three-dimensional T1-weighted magnetic resonance images (3D-T1WIs) of 21 healthy subjects were obtained and evaluated for effect of scanner in cortex volumetry. 3D-T1WIs of the 21 subjects were obtained with five MRI systems. Imaging of each subject was performed on each of five different MRI scanners. We used the Voxel-Based Morphometry 8 tool implemented in Statistical Parametric Mapping 8 and WFU PickAtlas software (Talairach brain atlas theory). The following software default settings were used as bilateral region-of-interest labels: "Frontal Lobe," "Hippocampus," "Occipital Lobe," "Orbital Gyrus," "Parietal Lobe," "Putamen," and "Temporal Lobe." Effect of scanner for cortex volumetry using the atlas-based method was reduced with DARTEL normalization compared with standard normalization in Frontal Lobe, Occipital Lobe, Orbital Gyrus, Putamen, and Temporal Lobe; was the same in Hippocampus and Parietal Lobe; and showed no increase with DARTEL normalization for any region of interest (ROI). DARTEL normalization reduces the effect of scanner, which is a major problem in multicenter studies.

  18. Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra provides reduced effect of scanner for cortex volumetry with atlas-based method in healthy subjects

    International Nuclear Information System (INIS)

    Goto, Masami; Ino, Kenji; Yano, Keiichi; Abe, Osamu; Aoki, Shigeki; Hayashi, Naoto; Miyati, Tosiaki; Takao, Hidemasa; Mori, Harushi; Kunimatsu, Akira; Ohtomo, Kuni; Iwatsubo, Takeshi; Yamashita, Fumio; Matsuda, Hiroshi

    2013-01-01

    This study aimed to investigate whether the effect of scanner for cortex volumetry with atlas-based method is reduced using Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL) normalization compared with standard normalization. Three-dimensional T1-weighted magnetic resonance images (3D-T1WIs) of 21 healthy subjects were obtained and evaluated for effect of scanner in cortex volumetry. 3D-T1WIs of the 21 subjects were obtained with five MRI systems. Imaging of each subject was performed on each of five different MRI scanners. We used the Voxel-Based Morphometry 8 tool implemented in Statistical Parametric Mapping 8 and WFU PickAtlas software (Talairach brain atlas theory). The following software default settings were used as bilateral region-of-interest labels: ''Frontal Lobe,'' ''Hippocampus,'' ''Occipital Lobe,'' ''Orbital Gyrus,'' ''Parietal Lobe,'' ''Putamen,'' and ''Temporal Lobe.'' Effect of scanner for cortex volumetry using the atlas-based method was reduced with DARTEL normalization compared with standard normalization in Frontal Lobe, Occipital Lobe, Orbital Gyrus, Putamen, and Temporal Lobe; was the same in Hippocampus and Parietal Lobe; and showed no increase with DARTEL normalization for any region of interest (ROI). DARTEL normalization reduces the effect of scanner, which is a major problem in multicenter studies. (orig.)

  19. Gelfand-Dickey algebra and higher spin symmetries on T2

    International Nuclear Information System (INIS)

    Sedra, M.B.

    2007-08-01

    We focus in this work to renew the interest in higher conformal spins symmetries and their relations to quantum field theories and integrable models. We consider the extension of the conformal Frappat et al. symmetries containing the Virasoro and the Antoniadis et al. algebras as particular cases describing geometrically special diffeomorphisms of the two dimensional torus T 2 . We show in a consistent way, and explicitly, how one can extract these generalized symmetries from the Gelfand-Dickey algebra. The link with Liouville and Toda conformal field theories is established and various important properties are discussed. (author)

  20. Copper-catalyzed oxidative Heck reactions between alkyltrifluoroborates and vinyl arenes.

    Science.gov (United States)

    Liwosz, Timothy W; Chemler, Sherry R

    2013-06-21

    We report herein that potassium alkyltrifluoroborates can be utilized in oxidative Heck-type reactions with vinyl arenes. The reaction is catalyzed by a Cu(OTf)2/1,10-phenanthroline with MnO2 as the stoichiometric oxidant. In addition to the alkyl Heck, amination, esterification, and dimerization reactions of alkyltrifluoroborates are demonstrated under analogous reaction conditions. Evidence for an alkyl radical intermediate is presented.

  1. Collocation for diffeomorphic deformations in medical image registration

    DEFF Research Database (Denmark)

    Darkner, Sune; Pai, Akshay Sadananda Uppinakudru; Liptrot, Matthew George

    2018-01-01

    Diffeomorphic deformation is a popular choice in medical image registration. A fundamental property of diffeomorphisms is in vertibility, implying that once the relation between two points A to B is found, then the relation B to A is given per definition. Consistency is a measure of a numerical a...

  2. The Weyl approach to the representation theory of reflection equation algebra

    International Nuclear Information System (INIS)

    Saponov, P A

    2004-01-01

    The present paper deals with the representation theory of reflection equation algebra, connected to a Hecke type R-matrix. Up to some reasonable additional conditions, the R-matrix is arbitrary (not necessary originating from quantum groups). We suggest a universal method for constructing finite dimensional irreducible representations in the framework of the Weyl approach well known in the representation theory of classical Lie groups and algebras. With this method a series of irreducible modules is constructed. The modules are parametrized by Young diagrams. The spectrum of central elements s k Tr q L k is calculated in the single-row and single-column representations. A rule for the decomposition of the tensor product of modules into a direct sum of irreducible components is also suggested

  3. Perspectivas mecanisticas de reações organicas catalisadas por paladio : Heck, oxa-Heck e acoplamento de Buchwald-Hartwig por ESI-MS/MS

    OpenAIRE

    Boniek Gontijo Vaz

    2009-01-01

    Resumo: A espectrometria de Massas por eletronspray (ESI-MS) tornou-se um método prático para o estudo de mecanismos reacionais em solução. Neste trabalho importantes reações catalisadas por paládio: reação de Heck-Mizoroki, oxa-Heck e o acoplamento de Buchwald-Hartwig foram monitoradas por ESI-MS visando interceptar espécies que comprovam as atuais propostas mecanísticas ou que abram caminho para novas propostas para estas reações. O monitoramento das reações foi realizado no modo off-line, ...

  4. Colour-kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms

    Energy Technology Data Exchange (ETDEWEB)

    Fu, Chih-Hao; Krasnov, Kirill [School of Mathematical Sciences, The University of Nottingham,University Park, Nottingham NG7 2RD (United Kingdom)

    2017-01-17

    Colour-kinematics duality suggests that Yang-Mills (YM) theory possesses some hidden Lie algebraic structure. So far this structure has resisted understanding, apart from some progress in the self-dual sector. We show that there is indeed a Lie algebra behind the YM Feynman rules. The Lie algebra we uncover is the Drinfeld double of the Lie algebra of vector fields. More specifically, we show that the kinematic numerators following from the YM Feynman rules satisfy a version of the Jacobi identity, in that the Jacobiator of the bracket defined by the YM cubic vertex is cancelled by the contribution of the YM quartic vertex. We then show that this Jacobi-like identity is in fact the Jacobi identity of the Drinfeld double. All our considerations are off-shell. Our construction explains why numerators computed using the Feynman rules satisfy the colour-kinematics at four but not at higher numbers of points. It also suggests a way of modifying the Feynman rules so that the duality can continue to hold for an arbitrary number of gluons. Our construction stops short of producing explicit higher point numerators because of an absence of a certain property at four points. We comment on possible ways of correcting this, but leave the next word in the story to future work.

  5. Noether Current of the Surface Term of Einstein-Hilbert Action, Virasoro Algebra, and Entropy

    Directory of Open Access Journals (Sweden)

    Bibhas Ranjan Majhi

    2013-01-01

    Full Text Available A derivation of Noether current from the surface term of Einstein-Hilbert action is given. We show that the corresponding charge, calculated on the horizon, is related to the Bekenstein-Hawking entropy. Also using the charge, the same entropy is found based on the Virasoro algebra and Cardy formula approach. In this approach, the relevant diffeomorphisms are found by imposing a very simple physical argument: diffeomorphisms keep the horizon structure invariant. This complements similar earlier results (Majhi and Padmanabhan (2012 (arXiv:1204.1422 obtained from York-Gibbons-Hawking surface term. Finally we discuss the technical simplicities and improvements over the earlier attempts and also various important physical implications.

  6. New reflection matrices for the Uq(gl(m|n)) case

    International Nuclear Information System (INIS)

    Doikou, Anastasia; Karaiskos, Nikos

    2009-01-01

    We examine supersymmetric representations of the B-type Hecke algebra. We exploit such representations to obtain new non-diagonal solutions of the reflection equation associated with the super algebra U q (gl(m|n)). The boundary super algebra is briefly discussed and it is shown to be central to the supersymmetric realization of the B-type Hecke algebra. (letter)

  7. Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra provides reduced effect of scanner for cortex volumetry with atlas-based method in healthy subjects

    Energy Technology Data Exchange (ETDEWEB)

    Goto, Masami; Ino, Kenji; Yano, Keiichi [University of Tokyo Hospital, Department of Radiological Technology, Bunkyo-ku, Tokyo (Japan); Abe, Osamu [Nihon University School of Medicine, Department of Radiology, Itabashi-ku, Tokyo (Japan); Aoki, Shigeki [Juntendo University, Department of Radiology, Bunkyo-ku, Tokyo (Japan); Hayashi, Naoto [University of Tokyo Hospital, Department of Computational Diagnostic Radiology and Preventive Medicine, Bunkyo-ku, Tokyo (Japan); Miyati, Tosiaki [Kanazawa University, Graduate School of Medical Science, Kanazawa (Japan); Takao, Hidemasa; Mori, Harushi; Kunimatsu, Akira; Ohtomo, Kuni [University of Tokyo Hospital, Department of Radiology and Department of Computational Diagnostic Radiology and Preventive Medicine, Bunkyo-ku, Tokyo (Japan); Iwatsubo, Takeshi [University of Tokyo, Department of Neuropathology, Bunkyo-ku, Tokyo (Japan); Yamashita, Fumio [Iwate Medical University, Department of Radiology, Yahaba, Iwate (Japan); Matsuda, Hiroshi [Integrative Brain Imaging Center National Center of Neurology and Psychiatry, Department of Nuclear Medicine, Kodaira, Tokyo (Japan); Collaboration: Japanese Alzheimer' s Disease Neuroimaging Initiative

    2013-07-15

    This study aimed to investigate whether the effect of scanner for cortex volumetry with atlas-based method is reduced using Diffeomorphic Anatomical Registration Through Exponentiated Lie Algebra (DARTEL) normalization compared with standard normalization. Three-dimensional T1-weighted magnetic resonance images (3D-T1WIs) of 21 healthy subjects were obtained and evaluated for effect of scanner in cortex volumetry. 3D-T1WIs of the 21 subjects were obtained with five MRI systems. Imaging of each subject was performed on each of five different MRI scanners. We used the Voxel-Based Morphometry 8 tool implemented in Statistical Parametric Mapping 8 and WFU PickAtlas software (Talairach brain atlas theory). The following software default settings were used as bilateral region-of-interest labels: ''Frontal Lobe,'' ''Hippocampus,'' ''Occipital Lobe,'' ''Orbital Gyrus,'' ''Parietal Lobe,'' ''Putamen,'' and ''Temporal Lobe.'' Effect of scanner for cortex volumetry using the atlas-based method was reduced with DARTEL normalization compared with standard normalization in Frontal Lobe, Occipital Lobe, Orbital Gyrus, Putamen, and Temporal Lobe; was the same in Hippocampus and Parietal Lobe; and showed no increase with DARTEL normalization for any region of interest (ROI). DARTEL normalization reduces the effect of scanner, which is a major problem in multicenter studies. (orig.)

  8. Eigenvalues of the Laplacian and of the Hecke operators for PSL(2,Z)

    International Nuclear Information System (INIS)

    Steil, G.

    1994-03-01

    A new method is described to compute with high accuracy a large number of eigenvalues and eigenfunctions (Maass wave forms) of the Laplacian and of the Hecke operators for the modular group. It relies essentially on the theory of Hecke operators. The results of the computations confirm some important conjectures from number theory, namely Ramanujan-Petersson, Sato-Tate, and the conjecture that the discrete spectrum of the Laplacian be simple. Examples of the numerical data are included as a reference. The algorithm can be generalized to other non-cocompact but cofinite arithmetic groups, like Picard group PSL(2, Z)[i]) and Hecke triangle groups Γ(√2) and Γ(√3). (orig.)

  9. Deterioration of abstract reasoning ability in mild cognitive impairment and Alzheimer's disease: correlation with regional grey matter volume loss revealed by diffeomorphic anatomical registration through exponentiated lie algebra analysis

    International Nuclear Information System (INIS)

    Yoshiura, Takashi; Hiwatashi, Akio; Yamashita, Koji; Takayama, Yukihisa; Kamano, Norihiro; Honda, Hiroshi; Ohyagi, Yasumasa; Kira, Jun-ichi; Monji, Akira; Kawashima, Toshiro

    2011-01-01

    To determine which brain regions are relevant to deterioration in abstract reasoning as measured by Raven's Colored Progressive Matrices (CPM) in the context of dementia. MR images of 37 consecutive patients including 19 with Alzheimer's disease (AD) and 18 with amnestic mild cognitive impairment (aMCI) were retrospectively analyzed. All patients were administered the CPM. Regional grey matter (GM) volume was evaluated according to the regimens of voxel-based morphometry, during which a non-linear registration algorithm called Diffeomorphic Anatomical Registration Through Exponentiated Lie algebra was employed. Multiple regression analyses were used to map the regions where GM volumes were correlated with CPM scores. The strongest correlation with CPM scores was seen in the left middle frontal gyrus while a region with the largest volume was identified in the left superior temporal gyrus. Significant correlations were seen in 14 additional regions in the bilateral cerebral hemispheres and right cerebellum. Deterioration of abstract reasoning ability in AD and aMCI measured by CPM is related to GM loss in multiple regions, which is in close agreement with the results of previous activation studies. (orig.)

  10. The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case

    NARCIS (Netherlands)

    Koornwinder, T.H.

    2007-01-01

    Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics Abstract Zhedanov's algebra AW(3) is considered with explicit structure constants such that, in the basic representation, the first generator becomes the second order q-difference operator for the Askey-Wilson polynomials. It is

  11. A new formulation of non-relativistic diffeomorphism invariance

    Energy Technology Data Exchange (ETDEWEB)

    Banerjee, Rabin, E-mail: rabin@bose.res.in [S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake City, Kolkata-700 098 (India); Mitra, Arpita, E-mail: arpita12t@bose.res.in [S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake City, Kolkata-700 098 (India); Mukherjee, Pradip, E-mail: mukhpradip@gmail.com [Department of Physics, Barasat Government College, Barasat, West Bengal (India)

    2014-10-07

    We provide a new formulation of non-relativistic diffeomorphism invariance. It is generated by localising the usual global Galilean symmetry. The correspondence with the type of diffeomorphism invariant models currently in vogue in the theory of fractional quantum Hall effect has been discussed. Our construction is shown to open up a general approach of model building in theoretical condensed matter physics. Also, this formulation has the capacity of obtaining Newton–Cartan geometry from the gauge procedure.

  12. Back-breeding the aurochs: the Heck brothers, National Socialism and imagined geographies for nonhuman Lebensraum

    NARCIS (Netherlands)

    Driessen, C.P.G.; Lorimer, J.

    2016-01-01

    This chapter investigates the bio-geographical imaginations behind the animal 'back-breeding' programs carried out by Lutz and Heinz Heck - two influential German zoologists who ran Berlin and Munich zoos. Partly with close connections to and patronage from the National Socialist elite, the Heck

  13. Diffeomorphisms of elliptic 3-manifolds

    CERN Document Server

    Hong, Sungbok; McCullough, Darryl; Rubinstein, J Hyam

    2012-01-01

    This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle. The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small...

  14. Fast and versatile microwave-assisted intramolecular Heck reaction in peptide macrocyclization using microwave energy.

    Science.gov (United States)

    Byk, Gerardo; Cohen-Ohana, Mirit; Raichman, Daniel

    2006-01-01

    We have revisited the intramolecular Heck reaction and investigated the microwave-assisted macrocyclization on preformed peptides using a model series of ring-varying peptides acryloyl-Gly-[Gly](n)-Phe(4-I)NHR; n = 0-4. The method was applied to both solution and solid supported cyclizations. We demonstrate that the intramolecular Heck reaction can be performed in peptides both in solution and solid support using a modified domestic microwave within 1 to 30 minutes in DMF under reflux with moderate yields ranging from 15 to 25% for a scale between 2-45 mg of linear precursors. The approach was applied to the synthesis of a constrained biologically relevant peptidomimetic bearing an Arg-Gly-Asp (RGD) sequence. These results make the microwave-assisted Heck reaction an attractive renovated approach for peptidomimetics. Copyright 2006 Wiley Periodicals, Inc.

  15. Homological stability of diffeomorphism groups

    DEFF Research Database (Denmark)

    Berglund, Alexander; Madsen, Ib Henning

    2013-01-01

    In this paper we prove a stability theorem for block diffeomorphisms of 2d -dimensional manifolds that are connected sums of S d ×S d . Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet’s lemma of disjunction, we determine the homology of the classifying space ...

  16. Entropy for frame bundle systems and Grassmann bundle systems induced by a diffeomorphism

    Institute of Scientific and Technical Information of China (English)

    SUN; Weniang(孙文祥)

    2002-01-01

    ALiao hyperbolic diffeomorphism has equal measure entropy and topological entropy to that ofits induced systems on frame bundles and Grassmann bundles. This solves a problem Liao posed in 1996 forLiao hyperbolic diffeomorphisms.

  17. ε-neighbourhoods of orbits of parabolic diffeomorphisms and cohomological equations

    International Nuclear Information System (INIS)

    Resman, Maja

    2014-01-01

    In this article, we study the analyticity of (directed) areas of ε-neighbourhoods of orbits of parabolic germs. The article is motivated by the question of analytic classification using ε-neighbourhoods of orbits in the simplest formal class. We show that the coefficient in front of the ε 2 term in the asymptotic expansion in ε, which we call the principal part of the area, is a sectorially analytic function in the initial point of the orbit. It satisfies a cohomological equation similar to the standard trivialization equation for parabolic diffeomorphisms. We give necessary and sufficient conditions on a diffeomorphism f for the existence of a globally analytic solution of this equation. Furthermore, we introduce a new classification type for diffeomorphisms implied by this new equation and investigate the relative position of its classes with respect to the analytic classes. (paper)

  18. Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

    Science.gov (United States)

    Hernandez, Monica

    2017-12-01

    This paper proposes a method for primal-dual convex optimization in variational large deformation diffeomorphic metric mapping problems formulated with robust regularizers and robust image similarity metrics. The method is based on Chambolle and Pock primal-dual algorithm for solving general convex optimization problems. Diagonal preconditioning is used to ensure the convergence of the algorithm to the global minimum. We consider three robust regularizers liable to provide acceptable results in diffeomorphic registration: Huber, V-Huber and total generalized variation. The Huber norm is used in the image similarity term. The primal-dual equations are derived for the stationary and the non-stationary parameterizations of diffeomorphisms. The resulting algorithms have been implemented for running in the GPU using Cuda. For the most memory consuming methods, we have developed a multi-GPU implementation. The GPU implementations allowed us to perform an exhaustive evaluation study in NIREP and LPBA40 databases. The experiments showed that, for all the considered regularizers, the proposed method converges to diffeomorphic solutions while better preserving discontinuities at the boundaries of the objects compared to baseline diffeomorphic registration methods. In most cases, the evaluation showed a competitive performance for the robust regularizers, close to the performance of the baseline diffeomorphic registration methods.

  19. Deterioration of abstract reasoning ability in mild cognitive impairment and Alzheimer's disease: correlation with regional grey matter volume loss revealed by diffeomorphic anatomical registration through exponentiated lie algebra analysis

    Energy Technology Data Exchange (ETDEWEB)

    Yoshiura, Takashi; Hiwatashi, Akio; Yamashita, Koji; Takayama, Yukihisa; Kamano, Norihiro; Honda, Hiroshi [Kyushu University, Department of Clinical Radiology, Graduate School of Medical Sciences, 3-1-1 Maidashi, Higashi-ku, Fukuoka (Japan); Ohyagi, Yasumasa; Kira, Jun-ichi [Kyushu University, Department of Neurology, Graduate School of Medical Sciences, 3-1-1 Maidashi, Higashi-ku, Fukuoka (Japan); Monji, Akira; Kawashima, Toshiro [Kyushu University, Department of Neuropsychiatry, Graduate School of Medical Sciences, 3-1-1 Maidashi, Higashi-ku, Fukuoka (Japan)

    2011-02-15

    To determine which brain regions are relevant to deterioration in abstract reasoning as measured by Raven's Colored Progressive Matrices (CPM) in the context of dementia. MR images of 37 consecutive patients including 19 with Alzheimer's disease (AD) and 18 with amnestic mild cognitive impairment (aMCI) were retrospectively analyzed. All patients were administered the CPM. Regional grey matter (GM) volume was evaluated according to the regimens of voxel-based morphometry, during which a non-linear registration algorithm called Diffeomorphic Anatomical Registration Through Exponentiated Lie algebra was employed. Multiple regression analyses were used to map the regions where GM volumes were correlated with CPM scores. The strongest correlation with CPM scores was seen in the left middle frontal gyrus while a region with the largest volume was identified in the left superior temporal gyrus. Significant correlations were seen in 14 additional regions in the bilateral cerebral hemispheres and right cerebellum. Deterioration of abstract reasoning ability in AD and aMCI measured by CPM is related to GM loss in multiple regions, which is in close agreement with the results of previous activation studies. (orig.)

  20. Matsuda–Heck reaction with arenediazonium tosylates in water

    Directory of Open Access Journals (Sweden)

    Ksenia V. Kutonova

    2015-03-01

    Full Text Available An environmentally friendly Matsuda–Heck reaction with arenediazonium tosylates has been developed for the first time. A range of alkenes was arylated in good to quantitative yields in water. The reaction is significantly accelerated when carried out under microwave heating. The arylation of haloalkylacrylates with diazonium salts has been implemented for the first time.

  1. Bayesian estimation of regularization and atlas building in diffeomorphic image registration.

    Science.gov (United States)

    Zhang, Miaomiao; Singh, Nikhil; Fletcher, P Thomas

    2013-01-01

    This paper presents a generative Bayesian model for diffeomorphic image registration and atlas building. We develop an atlas estimation procedure that simultaneously estimates the parameters controlling the smoothness of the diffeomorphic transformations. To achieve this, we introduce a Monte Carlo Expectation Maximization algorithm, where the expectation step is approximated via Hamiltonian Monte Carlo sampling on the manifold of diffeomorphisms. An added benefit of this stochastic approach is that it can successfully solve difficult registration problems involving large deformations, where direct geodesic optimization fails. Using synthetic data generated from the forward model with known parameters, we demonstrate the ability of our model to successfully recover the atlas and regularization parameters. We also demonstrate the effectiveness of the proposed method in the atlas estimation problem for 3D brain images.

  2. The Heck reaction in the production of fine chemicals

    NARCIS (Netherlands)

    Vries, Johannes G. de

    2001-01-01

    An overview is given of the use of the Heck reaction for the production of fine chemicals. Five commercial products have been identified that are produced on a scale in excess of 1 ton/year. The herbicide Prosulfuron™ is produced via a Matsuda reaction of 2-sulfonatobenzenediazonium on

  3. Kneser-Hecke-operators in coding theory

    OpenAIRE

    Nebe, Gabriele

    2005-01-01

    The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code $C$ over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect $C$ in a codimension 1 subspace. The eigenspaces of this self-adjoint linear operator may be described in terms of a coding-theory analogue of the Siegel $\\Phi $-operator.

  4. On the perfectness of C^{∞,s}-diffeomorphism groups on a foliated manifold

    OpenAIRE

    Jacek Lech

    2008-01-01

    The notion of \\(C^{r,s}\\) and \\(C^{\\infty,s}\\)-diffeomorphisms is introduced. It is shown that the identity component of the group of leaf preserving \\(C^{\\infty,s}\\)-diffeomorphisms with compact supports is perfect. This result is a modification of the Mather and Epstein perfectness theorem.

  5. Diffeomorphisms, Anomalies and the Fefferman-Graham Ambiguity

    International Nuclear Information System (INIS)

    Schwimmer, A.; Theisen, S.

    2000-01-01

    Using the Weyl transfomations induced by diffeomorphisms we set up a cohomological problem for the Fefferman-Graham coefficients. The cohomologically nontrivial solutions remove the ambiguity and give the nonlocal terms in the effective action responsible for the trace anomalies. (author)

  6. Dynamics and bifurcations of random circle diffeomorphisms

    NARCIS (Netherlands)

    Zmarrou, H.; Homburg, A.J.

    2008-01-01

    We discuss iterates of random circle diffeomorphisms with identically distributed noise, where the noise is bounded and absolutely continuous. Using arguments of B. Deroin, V.A. Kleptsyn and A. Navas, we provide precise conditions under which random attracting fixed points or random attracting

  7. Palladium-Catalyzed Heck Coupling Reaction of Aryl Bromides in Aqueous Media Using Tetrahydropyrimidinium Salts as Carbene Ligands

    Directory of Open Access Journals (Sweden)

    İsmail Özdemir

    2010-01-01

    Full Text Available An efficient and stereoselective catalytic system for the Heck cross coupling reaction using novel 1,3-dialkyl-3,4,5,6-tetrahydropyrimidinium salts (1, LHX and Pd(OAc2 loading has been reported. The palladium complexes derived from the salts 1a-f prepared in situ exhibit good catalytic activity in the Heck coupling reaction of aryl bromides under mild conditions.

  8. On the uniform perfectness of equivariant diffeomorphism groups for principal G manifolds

    Directory of Open Access Journals (Sweden)

    Kazuhiko Fukui

    2017-01-01

    Full Text Available We proved in [K. Abe, K. Fukui, On commutators of equivariant diffeomorphisms, Proc. Japan Acad. 54 (1978, 52-54] that the identity component \\(\\text{Diff}\\,^r_{G,c}(M_0\\ of the group of equivariant \\(C^r\\-diffeomorphisms of a principal \\(G\\ bundle \\(M\\ over a manifold \\(B\\ is perfect for a compact connected Lie group \\(G\\ and \\(1 \\leq r \\leq \\infty\\ (\\(r \

  9. Mild and Efficient Nickel-Catalyzed Heck Reactions with Electron-Rich Olefins

    DEFF Research Database (Denmark)

    Gøgsig, Thomas; Kleimark, Jonatan; Lill, Sten O. Nilsson

    2012-01-01

    proved compatible, and the corresponding aryl methyl ketone could be secured after hydrolysis in yields approaching quantitative. Good functional group tolerance was observed matching the characteristics of the analogous Pd-catalyzed Heck reaction. The high levels of catalytic activity were explained...

  10. p-Forms and diffeomorphisms: Hamiltonian formulation

    Science.gov (United States)

    Baulieu, Laurent; Henneaux, Marc

    1987-07-01

    The BRST charges corresponding to various (equivalent) ways of writing the action of the diffeomorphism group on p-form gauge fields are canonically related by a canonical transformation in the extended phase space which is explicitly constructed. The occurrence of higher order structure functions is pointed out. Also at: Centro de Estudios Cientificos de Santiago, Casilla 16443, Santiago 9, Chile.

  11. Periodic diffeomorphisms on homotopy E (4) surfaces

    Indian Academy of Sciences (India)

    Home; Journals; Proceedings – Mathematical Sciences; Volume 124; Issue 3. Periodic Diffeomorphisms on Homotopy (4) Surfaces. Hongxia Li. Volume 124 Issue 3 August 2014 pp 437-445. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/pmsc/124/03/0437-0445 ...

  12. Circle diffeomorphisms forced by expanding circle maps

    NARCIS (Netherlands)

    Homburg, A.J.

    2012-01-01

    We discuss the dynamics of skew product maps defined by circle diffeomorphisms forced by expanding circle maps. We construct an open class of such systems that are robustly topologically mixing and for which almost all points in the same fiber converge under iteration. This property follows from the

  13. Supported liquid phase catalyst coating in micro flow Mizoroki-Heck reaction

    NARCIS (Netherlands)

    Stouten, S.C.; Noël, T.; Wang, Q.; Hessel, V.

    2015-01-01

    A Supported Liquid Phase Catalyst (SLPC) coating was successfully applied for the Mizoroki–Heck reaction in micro flow. Foremost, extended on stream operation was enabled and the on stream performance stability was verified. Stable catalytic activity was achieved during two consecutive runs totaling

  14. Synthesis of novel room temperature chiral ionic liquids: application as reaction media for the heck arylation of aza-endocyclic acrylates

    Energy Technology Data Exchange (ETDEWEB)

    Pastre, Julio C.; Correia, Carlos R.D., E-mail: genisson@chimie.ups-tlse.f, E-mail: roque@iqm.unicamp.b [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Inst. de Quimica; Genisson, Yves [Universite Paul Sabatier, Toulouse (France). Lab. de Synthese et Physicochimie des Molecules d' Interet Biologique; Saffon, Nathalie [Universite Paul Sabatier, Toulouse (France). Structure federative toulousaine en chimie moleculaire (SFTCM); Dandurand, Jany [Universite Paul Sabatier, Toulouse (France). Lab. de Physique des Polymeres

    2010-07-01

    New achiral and chiral RTILs were prepared using novel and/or optimized synthetic routes. These new series of imidazolinium, imidazolium, pyridinium and nicotine-derived ionic liquids were fully characterized including differential scanning calorimetry (DSC) analysis. The performance of these achiral and chiral room temperature ionic liquids (RTILs) was demonstrated by means of the Heck arylation of endocyclic acrylates employing arenediazonium salts and aryl iodides. The Heck arylations performed in the presence of these ionic entities, either as a solvent or as an additive, were effective leading to complete conversion of the substrate and good to excellent yield of the Heck adduct. In spite of the good performances, no asymmetric induction was observed in any of the cases studied. Two new diastereoisomeric NHC-palladium complexes were prepared in good yields from a chiral imidazolium salt and their structure characterized by X-ray diffraction. Overall, the Heck arylations employing arenediazonium tetrafluoroborates in RTILs were more effective than the traditional protocols employing aryl iodides in terms of reactivity and yields. (author)

  15. Hiperplasia epitelial focal (doença de Heck em descendente de índios brasileiros: relato de caso Focal epithelial hyperplasia (Heck's disease in Brazilian indian descent: report of a case

    Directory of Open Access Journals (Sweden)

    Pedro Paulo de Andrade Santos

    2007-12-01

    Full Text Available A hiperplasia epitelial focal, ou doença de Heck, é uma enfermidade rara, benigna, que afeta a mucosa oral de crianças e adultos jovens de diversas regiões do mundo e em diferentes grupos étnicos, como indígenas e esquimós. Apresenta correlação com o papilomavírus humano (HPV no qual os tipos 13 e 32 têm sido consistentemente detectados nessas lesões. Este artigo relata um caso de uma paciente de 18 anos de idade, descendente de índios potiguares, que compareceu ao serviço de estomatologia da Universidade Federal do Rio Grande do Norte (UFRN, exibindo lesões bem definidas, arredondadas, planas, localizadas em cavidade oral, com tempo de evolução de aproximadamente dois anos. As lesões foram submetidas a biópsias incisionais, constatado-se no exame histopatológico alterações epiteliais, como acantose, cristas epiteliais em forma de "taco de golfe" além de células mitosóides. Esses achados histopatológicos foram compatíveis com a hipótese clínica de hiperplasia epitelial focal (doença de Heck.The focal epithelial hyperplasia or Heck's disease is a benign rare pathology, that affects children and young adults oral mucosal in many world regions, and different ethnic groups, for example Indians and Eskimos. Presents correlation with the subtypes 13 and 32 of human papillomavirus (HPV. This article report a case of an 18-year-old patient, descent of potiguar indian, attended in stomatology service of Federal University of Rio Grande do Norte (UFRN, presenting well defined lesions, round, plane, localized in oral cavity with an evolution of two years. The lesions were submitted to incisional biopsies, verifying in histopathologic exam, epithelial alterations, like acanthosis, epithelial projections in "parquet block of golf" beyond mitosoid cells. These histopathological findings were compatible with clinical hypothesis of focal epithelial hyperplasia (Heck's disease.

  16. Pesin’s entropy formula for stochastic flows of diffeomorphisms

    Institute of Scientific and Technical Information of China (English)

    刘培东

    1996-01-01

    Pesin’s entropy formula relating entropy and Lyapunov exponents within the context of random dynamical systems generated by (discrete or continuous) stochastic flows of diffeomorphisms (including solution flows of stochastic differential equations on manifolds) is proved.

  17. Accelerated Optimization in the PDE Framework: Formulations for the Manifold of Diffeomorphisms

    KAUST Repository

    Sundaramoorthi, Ganesh

    2018-04-04

    We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by generalizing Nesterov accelerated optimization to the manifold of diffeomorphisms. While our framework is general for infinite dimensional manifolds, we specifically treat the case of diffeomorphisms, motivated by optical flow problems in computer vision. This is accomplished by building on a recent variational approach to a general class of accelerated optimization methods by Wibisono, Wilson and Jordan, which applies in finite dimensions. We generalize that approach to infinite dimensional manifolds. We derive the surprisingly simple continuum evolution equations, which are partial differential equations, for accelerated gradient descent, and relate it to simple mechanical principles from fluid mechanics. Our approach has natural connections to the optimal mass transport problem. This is because one can think of our approach as an evolution of an infinite number of particles endowed with mass (represented with a mass density) that moves in an energy landscape. The mass evolves with the optimization variable, and endows the particles with dynamics. This is different than the finite dimensional case where only a single particle moves and hence the dynamics does not depend on the mass. We derive the theory, compute the PDEs for accelerated optimization, and illustrate the behavior of these new accelerated optimization schemes.

  18. Accelerated Optimization in the PDE Framework: Formulations for the Manifold of Diffeomorphisms

    KAUST Repository

    Sundaramoorthi, Ganesh; Yezzi, Anthony

    2018-01-01

    We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by generalizing Nesterov accelerated optimization to the manifold of diffeomorphisms. While our framework is general for infinite dimensional manifolds, we specifically treat the case of diffeomorphisms, motivated by optical flow problems in computer vision. This is accomplished by building on a recent variational approach to a general class of accelerated optimization methods by Wibisono, Wilson and Jordan, which applies in finite dimensions. We generalize that approach to infinite dimensional manifolds. We derive the surprisingly simple continuum evolution equations, which are partial differential equations, for accelerated gradient descent, and relate it to simple mechanical principles from fluid mechanics. Our approach has natural connections to the optimal mass transport problem. This is because one can think of our approach as an evolution of an infinite number of particles endowed with mass (represented with a mass density) that moves in an energy landscape. The mass evolves with the optimization variable, and endows the particles with dynamics. This is different than the finite dimensional case where only a single particle moves and hence the dynamics does not depend on the mass. We derive the theory, compute the PDEs for accelerated optimization, and illustrate the behavior of these new accelerated optimization schemes.

  19. An Intramolecular Heck reaction that Prefers a 5-endo- to a 6-exo-trig Cyclization Pathway

    DEFF Research Database (Denmark)

    Vital, Paulo; Norrby, Per-Ola; Tanner, David Ackland

    2006-01-01

    A regioselective aromatic Claisen rearrangement was used to prepare 17a, the precursor of triflate 17e. The intramolecular Heck reaction of 17e is promoted only by bidentate phosphine ligands, giving exclusively and in excellent yield 20, the product of a 5-endo-trig cyclization, despite the poss......A regioselective aromatic Claisen rearrangement was used to prepare 17a, the precursor of triflate 17e. The intramolecular Heck reaction of 17e is promoted only by bidentate phosphine ligands, giving exclusively and in excellent yield 20, the product of a 5-endo-trig cyclization, despite...

  20. On the fourth moment of Hecke Maass forms and the Random Wave Conjecture

    OpenAIRE

    Buttcane, Jack; Khan, Rizwanur

    2016-01-01

    Conditionally on the Generalized Lindel\\"of Hypothesis, we obtain an asymptotic for the fourth moment of Hecke Maass cusp forms of large Laplacian eigenvalue for the full modular group. This lends support to the Random Wave Conjecture.

  1. Breaking the regioselectivity rule for acrylate insertion in the Mizoroki-Heck reaction.

    Science.gov (United States)

    Wucher, Philipp; Caporaso, Lucia; Roesle, Philipp; Ragone, Francesco; Cavallo, Luigi; Mecking, Stefan; Göttker-Schnetmann, Inigo

    2011-05-31

    In modern methods for the preparation of small molecules and polymers, the insertion of substrate carbon-carbon double bonds into metal-carbon bonds is a fundamental step of paramount importance. This issue is illustrated by Mizoroki-Heck coupling as the most prominent example in organic synthesis and also by catalytic insertion polymerization. For unsymmetric substrates H(2)C = CHX the regioselectivity of insertion is decisive for the nature of the product formed. Electron-deficient olefins insert selectively in a 2,1-fashion for electronic reasons. A means for controlling this regioselectivity is lacking to date. In a combined experimental and theoretical study, we now report that, by destabilizing the transition state of 2,1-insertion via steric interactions, the regioselectivity of methyl acrylate insertion into palladium-methyl and phenyl bonds can be inverted entirely to yield the opposite "regioirregular" products in stoichiometric reactions. Insights from these experiments will aid the rational design of complexes which enable a catalytic and regioirregular Mizoroki-Heck reaction of electron-deficient olefins.

  2. Diffeomorphisms as symplectomorphisms in history phase space: Bosonic string model

    International Nuclear Information System (INIS)

    Kouletsis, I.; Kuchar, K.V.

    2002-01-01

    The structure of the history phase space G of a covariant field system and its history group (in the sense of Isham and Linden) is analyzed on an example of a bosonic string. The history space G includes the time map T from the spacetime manifold (the two-sheet) Y to a one-dimensional time manifold T as one of its configuration variables. A canonical history action is posited on G such that its restriction to the configuration history space yields the familiar Polyakov action. The standard Dirac-ADM action is shown to be identical with the canonical history action, the only difference being that the underlying action is expressed in two different coordinate charts on G. The canonical history action encompasses all individual Dirac-ADM actions corresponding to different choices T of foliating Y. The history Poisson brackets of spacetime fields on G induce the ordinary Poisson brackets of spatial fields in the instantaneous phase space G 0 of the Dirac-ADM formalism. The canonical history action is manifestly invariant both under spacetime diffeomorphisms Diff Y and temporal diffeomorphisms Diff T. Both of these diffeomorphisms are explicitly represented by symplectomorphisms on the history phase space G. The resulting classical history phase space formalism is offered as a starting point for projection operator quantization and consistent histories interpretation of the bosonic string model

  3. Discrimination of dementia with Lewy bodies from Alzheimer's disease using voxel-based morphometry of white matter by statistical parametric mapping 8 plus diffeomorphic anatomic registration through exponentiated Lie algebra.

    Science.gov (United States)

    Nakatsuka, Tomoya; Imabayashi, Etsuko; Matsuda, Hiroshi; Sakakibara, Ryuji; Inaoka, Tsutomu; Terada, Hitoshi

    2013-05-01

    The purpose of this study was to identify brain atrophy specific for dementia with Lewy bodies (DLB) and to evaluate the discriminatory performance of this specific atrophy between DLB and Alzheimer's disease (AD). We retrospectively reviewed 60 DLB and 30 AD patients who had undergone 3D T1-weighted MRI. We randomly divided the DLB patients into two equal groups (A and B). First, we obtained a target volume of interest (VOI) for DLB-specific atrophy using correlation analysis of the percentage rate of significant whole white matter (WM) atrophy calculated using the Voxel-based Specific Regional Analysis System for Alzheimer's Disease (VSRAD) based on statistical parametric mapping 8 (SPM8) plus diffeomorphic anatomic registration through exponentiated Lie algebra, with segmented WM images in group A. We then evaluated the usefulness of this target VOI for discriminating the remaining 30 DLB patients in group B from the 30 AD patients. Z score values in this target VOI obtained from VSRAD were used as the determinant in receiver operating characteristic (ROC) analysis. Specific target VOIs for DLB were determined in the right-side dominant dorsal midbrain, right-side dominant dorsal pons, and bilateral cerebellum. ROC analysis revealed that the target VOI limited to the midbrain exhibited the highest area under the ROC curves of 0.75. DLB patients showed specific atrophy in the midbrain, pons, and cerebellum. Midbrain atrophy demonstrated the highest power for discriminating DLB and AD. This approach may be useful for determining the contributions of DLB and AD pathologies to the dementia syndrome.

  4. Diffeomorphic image registration with automatic time-step adjustment

    DEFF Research Database (Denmark)

    Pai, Akshay Sadananda Uppinakudru; Klein, S.; Sommer, Stefan Horst

    2015-01-01

    In this paper, we propose an automated Euler's time-step adjustment scheme for diffeomorphic image registration using stationary velocity fields (SVFs). The proposed variational problem aims at bounding the inverse consistency error by adaptively adjusting the number of Euler's step required to r...... accuracy as a fixed time-step scheme however at a much less computational cost....

  5. Asymptotic symmetries on the Kerr-Newman horizon without the anomaly of diffeomorphism invariance

    International Nuclear Information System (INIS)

    Koga, Jun-ichirou

    2008-01-01

    We analyze asymptotic symmetries on the Killing horizon of the four-dimensional Kerr-Newman black hole. We first derive the asymptotic Killing vectors on the Killing horizon, which describe the asymptotic symmetries, and find that the general form of these asymptotic Killing vectors is the universal one possessed by arbitrary Killing horizons. We then construct the phase space associated with the asymptotic symmetries. It is shown that the phase space of an extreme black hole either has the size comparable with a non-extreme black hole, or is small enough to exclude degeneracy, depending on whether or not the global structure of a Killing horizon particular to an extreme black hole is respected. We also show that the classical central charge in the Poisson brackets algebra of these asymptotic symmetries vanishes, which implies that there is not an anomaly of diffeomorphism invariance. By taking into account other results in the literature, we argue that the vanishing central charge on a black hole horizon, in an effective theory, looks consistent with the thermal feature of a black hole. We furthermore argue that the vanishing central charge implies that there are sufficiently many classical configurations that constitute a single macroscopic state, while these configurations are distinguished physically

  6. Non-stationary compositions of Anosov diffeomorphisms

    International Nuclear Information System (INIS)

    Stenlund, Mikko

    2011-01-01

    Motivated by non-equilibrium phenomena in nature, we study dynamical systems whose time-evolution is determined by non-stationary compositions of chaotic maps. The constituent maps are topologically transitive Anosov diffeomorphisms on a two-dimensional compact Riemannian manifold, which are allowed to change with time—slowly, but in a rather arbitrary fashion. In particular, such systems admit no invariant measure. By constructing a coupling, we prove that any two sufficiently regular distributions of the initial state converge exponentially with time. Thus, a system of this kind loses memory of its statistical history rapidly

  7. Magnetically Separable Fe3O4@DOPA-Pd: A Heterogeneous Catalyst for Aqueous Heck Reaction

    Science.gov (United States)

    Magnetically separable Fe3O4@DOPA-Pd catalyst has been synthesized via anchoring of palladium over dopamine-coated magnetite via non-covalent interaction and the catalyst is utilized for expeditious Heck coupling in aqueous media.

  8. Reactivity and Regioselectivity in the Heck Reaction - A Hammett Study of 4-Substituted Styrenes

    DEFF Research Database (Denmark)

    Fristrup, Peter; Le Quement, Sebastian; Tanner, David Ackland

    2004-01-01

    The regioselectivity in the cationic Heck reaction of 4-substituted styrenes was addressed by a Hammett study. In this branching reaction, plots based on the substrate reactivity did not give meaningful data, whereas the product distribution was variable due to differing preferences for further...

  9. The Koslowski–Sahlmann representation: gauge and diffeomorphism invariance

    International Nuclear Information System (INIS)

    Campiglia, Miguel; Varadarajan, Madhavan

    2014-01-01

    The discrete spatial geometry underlying loop quantum gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non-degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalized the LQG representation so as to describe states labeled by smooth non-degenerate triad fields. His representation was further studied by Sahlmann with a view to imposing gauge and spatial diffeomorphism invariance through group averaging methods. Motivated by the desire to model asymptotically flat quantum geometry by states with triad labels which are non-degenerate at infinity but not necessarily so in the interior, we initiate a generalization of Sahlmann’s considerations to triads of varying degeneracy. In doing so, we include delicate phase contributions to the averaging procedure which are crucial for the correct implementation of the gauge and diffeomorphism constraints, and whose existence can be traced to the background exponential functions recently constructed by one of us. Our treatment emphasizes the role of symmetries of quantum states in the averaging procedure. Semianalyticity, influential in the proofs of the beautiful uniqueness results for LQG, plays a key role in our considerations. As a by product, we re-derive the group averaging map for standard LQG, highlighting the role of state symmetries and explicitly exhibiting the essential uniqueness of its specification. (paper)

  10. Renormalization in quantum field theory and the Riemann-Hilbert problem. I. Hopf algebra structure of graphs and the main theorem

    International Nuclear Information System (INIS)

    Connes, A.; Kreimer, D.

    2000-01-01

    This paper gives a complete selfcontained proof of our result (1999) showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra H which is commutative asan algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra G whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of H. We show then that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop γ(z) element of G, z element of C, where C is a small circle of complex dimensions around the integer dimension D of space-time. Our main result is that the renormalized theory is just the evaluation at z=D of the holomorphic part γ + of the Birkhoff decomposition of γ. We begin to analyse the group G and show that it is a semi-direct product of an easily understood abelian group by a highly non-trivial group closely tied up with groups of diffeomorphisms. (orig.)

  11. A connection between the Einstein and Yang-Mills equations

    International Nuclear Information System (INIS)

    Mason, L.J.; Newman, E.T.

    1989-01-01

    It is our purpose here to show an unusual relationship between the Einstein equations and the Yang-Mills equations. We give a correspondence between solutions of the self-dual Einstein vacuum equations and the self-dual Yang-Mills equations with a special choice of gauge group. The extension of the argument to the full Yang-Mills equations yields Einstein's unified equations. We try to incorporate the full Einstein vacuum equations, but the approach is incomplete. We first consider Yang-Mills theory for an arbitrary Lie-algebra with the condition that the connection 1-form and curvature are constant on Minkowski space. This leads to a set of algebraic equations on the connection components. We then specialize the Lie-algebra to be the (infinite dimensional) Lie algebra of a group of diffeomorphisms of some manifold. The algebraic equations then become differential equations for four vector fields on the manifold on which the diffeomorphisms act. In the self-dual case, if we choose the connection components from the Lie-algebra of the volume preserving 4-dimensional diffeomorphism group, the resulting equations are the same as those obtained by Ashtekar, Jacobsen and Smolin, in their remarkable simplification of the self-dual Einstein vacuum equations. (An alternative derivation of the same equations begins with the self-dual Yang-Mills connection now depending only on the time, then choosing the Lie-algebra as that of the volume preserving 3-dimensional diffeomorphisms). When the reduced full Yang-Mills equations are used in the same context, we get Einstein's equations for his unified theory based on absolute parallelism. To incorporate the full Einstein vacuum equations we use as the Lie group the semi-direct product of the diffeomorphism group of a 4-dimensional manifold with the group of frame rotations of an SO(1, 3) bundle over the 4-manifold. This last approach, however, yields equations more general than the vacuum equations. (orig.)

  12. Whole brain diffeomorphic metric mapping via integration of sulcal and gyral curves, cortical surfaces, and images

    Science.gov (United States)

    Du, Jia; Younes, Laurent; Qiu, Anqi

    2011-01-01

    This paper introduces a novel large deformation diffeomorphic metric mapping algorithm for whole brain registration where sulcal and gyral curves, cortical surfaces, and intensity images are simultaneously carried from one subject to another through a flow of diffeomorphisms. To the best of our knowledge, this is the first time that the diffeomorphic metric from one brain to another is derived in a shape space of intensity images and point sets (such as curves and surfaces) in a unified manner. We describe the Euler–Lagrange equation associated with this algorithm with respect to momentum, a linear transformation of the velocity vector field of the diffeomorphic flow. The numerical implementation for solving this variational problem, which involves large-scale kernel convolution in an irregular grid, is made feasible by introducing a class of computationally friendly kernels. We apply this algorithm to align magnetic resonance brain data. Our whole brain mapping results show that our algorithm outperforms the image-based LDDMM algorithm in terms of the mapping accuracy of gyral/sulcal curves, sulcal regions, and cortical and subcortical segmentation. Moreover, our algorithm provides better whole brain alignment than combined volumetric and surface registration (Postelnicu et al., 2009) and hierarchical attribute matching mechanism for elastic registration (HAMMER) (Shen and Davatzikos, 2002) in terms of cortical and subcortical volume segmentation. PMID:21281722

  13. Regularized inner products and weakly holomorphic Hecke eigenforms

    Science.gov (United States)

    Bringmann, Kathrin; Kane, Ben

    2018-01-01

    We show that the image of repeated differentiation on weak cusp forms is precisely the subspace which is orthogonal to the space of weakly holomorphic modular forms. This gives a new interpretation of weakly holomorphic Hecke eigenforms. The research of the first author is supported by the Alfried Krupp Prize for Young University Teachers of the Krupp foundation and the research leading to these results receives funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant agreement n. 335220—AQSER. The research of the second author was supported by grants from the Research Grants Council of the Hong Kong SAR, China (project numbers HKU 27300314, 17302515, and 17316416).

  14. Encaging palladium(0 in layered double hydroxide: A sustainable catalyst for solvent-free and ligand-free Heck reaction in a ball mill

    Directory of Open Access Journals (Sweden)

    Wei Shi

    2017-08-01

    Full Text Available In this paper, the synthesis of a cheap, reusable and ligand-free Pd catalyst supported on MgAl layered double hydroxides (Pd/MgAl-LDHs by co-precipitation and reduction methods is described. The catalyst was used in Heck reactions under high-speed ball milling (HSBM conditions at room temperature. The effects of milling-ball size, milling-ball filling degree, reaction time, rotation speed and grinding auxiliary category, which would influence the yields of mechanochemical Heck reactions, were investigated in detail. The characterization results of XRD, ICP–MS and XPS suggest that Pd/MgAl-LDHs have excellent textural properties with zero-valence Pd on its layers. The reaction results indicate that the catalyst could be utilized in HSBM systems to afford a wide range of Heck coupling products in satisfactory yields. Furthermore, this catalyst could be easily recovered and reused for at least five times without significant loss of catalytic activity.

  15. Hecke algebras and harmonic analysis

    NARCIS (Netherlands)

    Opdam, E.M.; Sanz-Solé, M.; Soria, J.; Varona, J.L.; Verdera, J.

    2006-01-01

    The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world, and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize

  16. Design, Testing and Kinetic Analysis of Bulky Monodentate Phosphorus Ligands in the Mizoroki-Heck Reaction

    NARCIS (Netherlands)

    Dodds, Deborah L.; Boele, Maarten D. K.; van Strijdonck, Gino P. F.; de Vries, Johannes G.; van Leeuwen, Piet W. N. M.; Kamer, Paul C. J.

    A series of new monodentate phosphane ligands 2 have been evaluated in the MizorokiHeck arylation reaction of iodobenzene and styrene and compared with our previously reported ligands, 1, 3 and 4. The concept of rational ligand design is discussed, and we describe how the performance of this new

  17. Palladium(II-catalyzed Heck reaction of aryl halides and arylboronic acids with olefins under mild conditions

    Directory of Open Access Journals (Sweden)

    Tanveer Mahamadali Shaikh

    2013-08-01

    Full Text Available A series of general and selective Pd(II-catalyzed Heck reactions were investigated under mild reaction conditions. The first protocol has been developed employing an imidazole-based secondary phosphine oxide (SPO ligated palladium complex (6 as a precatalyst. The catalytic coupling of aryl halides and olefins led to the formation of the corresponding coupled products in excellent yields. A variety of substrates, both electron-rich and electron-poor olefins, were converted smoothly to the targeted products in high yields. Compared with the existing approaches employing SPO–Pd complexes in a Heck reaction, the current strategy features mild reaction conditions and broad substrate scope. Furthermore, we described the coupling of arylboronic acids with olefins, which were catalyzed by Pd(OAc2 and employed N-bromosuccinimide as an additive under ambient conditions. The resulted biaryls have been obtained in moderate to good yields.

  18. Carbonylative Heck Reactions Using CO Generated ex Situ in a Two-Chamber System

    DEFF Research Database (Denmark)

    Hermange, Philippe; Gøgsig, Thomas; Lindhardt, Anders Thyboe

    2011-01-01

    A carbonylative Heck reaction of aryl iodides and styrene derivatives employing a two-chamber system using a stable, crystalline, and nontransition metal based carbon monoxide source is reported. By applying near-stoichiometric amounts of the carbon monoxide precursor, an effective exploitation o...... of the hazardous CO gas is obtained affording chalcone derivatives in good yields. Application to isotope labeling, incorporating 13CO, was further established....

  19. Fast Template-based Shape Analysis using Diffeomorphic Iterative Centroid

    OpenAIRE

    Cury , Claire; Glaunès , Joan Alexis; Chupin , Marie; Colliot , Olivier

    2014-01-01

    International audience; A common approach for the analysis of anatomical variability relies on the estimation of a representative template of the population, followed by the study of this population based on the parameters of the deformations going from the template to the population. The Large Deformation Diffeomorphic Metric Mapping framework is widely used for shape analysis of anatomical structures, but computing a template with such framework is computationally expensive. In this paper w...

  20. Fourier transforms related to a root system of rank 1.

    NARCIS (Netherlands)

    Groenevelt, W.G.M.

    2007-01-01

    Abstract : We introduce an algebra $\\mathcal H$ consisting of difference-reflection operators and multiplication operators that can be considered as a q = 1 analogue of Sahi's double affine Hecke algebra related to the affine root system of type $(C^\\vee_1, C_1)$ . We study eigenfunctions of a

  1. Vertex algebras and algebraic curves

    CERN Document Server

    Frenkel, Edward

    2004-01-01

    Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book co...

  2. Algebraic partial Boolean algebras

    International Nuclear Information System (INIS)

    Smith, Derek

    2003-01-01

    Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A 5 sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E 8

  3. Preparation and Characterization of Pd Modified TiO2 Nanofiber Catalyst for Carbon–Carbon Coupling Heck Reaction

    Directory of Open Access Journals (Sweden)

    Leah O. Nyangasi

    2017-01-01

    Full Text Available TiO2 fibers were prepared through electrospinning of poly methyl methacrylate (PMMA and titanium isopropoxide (TIP solution followed by calcination of fibers in air at 500°C. Cetyltrimethylammonium bromide (CTAB protected palladium nanoparticles (Pd NPs prepared through reduction method were successfully adsorbed on the TiO2 nanofibers (NF. Combined studies of X-ray diffraction (XRD, scanning electron microscope (SEM, and transmission electron microscope (TEM indicated that the synthesized Pd/TiO2 had anatase. BET indicated that the synthesized TiO2 and Pd/TiO2 had a surface area of 53.4 and 43.4 m2/g, respectively. The activity and selectivity of 1 mol% Pd/TiO2 in the Heck reaction have been investigated towards the Mizoroki-Heck carbon–carbon cross-coupling of bromobenzene (ArBr and styrene. Temperature, time, solvent, and base were optimized and catalyst was recycled thrice. 1H NMR and 13C NMR indicated that stilbene, a known compound from literature, was obtained in various Heck reactions at temperatures between 100°C and 140°C but the recyclability was limited due to some palladium leaching and catalyst poisoning which probably arose from some residual carbon from the polymer. The catalyst was found to be highly active under air atmosphere with reaction temperatures up to 140°C. Optimized reaction condition resulted in 89.7% conversions with a TON of 1993.4 and TOF value of 332.2 hr−1.

  4. Linear Algebra and Smarandache Linear Algebra

    OpenAIRE

    Vasantha, Kandasamy

    2003-01-01

    The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and vector spaces over finite p...

  5. Introduction to vertex algebras, Borcherds algebras and the Monster Lie algebras

    International Nuclear Information System (INIS)

    Gebert, R.W.

    1993-09-01

    The theory of vertex algebras constitutes a mathematically rigorous axiomatic formulation of the algebraic origins of conformal field theory. In this context Borcherds algebras arise as certain ''physical'' subspaces of vertex algebras. The aim of this review is to give a pedagogical introduction into this rapidly-developing area of mathematics. Based on the machinery of formal calculus we present the axiomatic definition of vertex algebras. We discuss the connection with conformal field theory by deriving important implications of these axioms. In particular, many explicit calculations are presented to stress the eminent role of the Jacobi identity axiom for vertex algebras. As a class of concrete examples the vertex algebras associated with even lattices are constructed and it is shown in detail how affine Lie algebras and the fake Monster Lie algebra naturally appear. This leads us to the abstract definition of Borcherds algebras as generalized Kac-Moody algebras and their basic properties. Finally, the results about the simplest generic Borcherds algebras are analysed from the point of view of symmetry in quantum theory and the construction of the Monster Lie algebra is sketched. (orig.)

  6. Diphosphinoazine Palladium(II) Complexes as Catalysts for the Heck Reaction of Bromides and an Activated Chloride

    Czech Academy of Sciences Publication Activity Database

    Včelák, Jaroslav; Storch, Jan; Czakoová, Marie; Čermák, Jan

    2004-01-01

    Roč. 222, 1-2 (2004), s. 121-126 ISSN 1381-1169 R&D Projects: GA ČR GA203/01/0554; GA AV ČR IAA4072205 Institutional research plan: CEZ:AV0Z4072921 Keywords : heck reaction * amido complex es * palladium Subject RIV: CA - Inorganic Chemistry Impact factor: 2.316, year: 2004

  7. Breaking diffeomorphism invariance and tests for the emergence of gravity

    International Nuclear Information System (INIS)

    Anber, Mohamed M.; Aydemir, Ufuk; Donoghue, John F.

    2010-01-01

    If general relativity is an emergent phenomenon, there may be small violations of diffeomorphism invariance. We propose a phenomenology of perturbatively small violations of general relativity by the inclusion of terms which break general covariance. These can be tested by matching to the parameterized post-Newtonian formalism. The most sensitive tests involve pulsar timing and provide an extremely strong bound, with a dimensionless constraint of order 10 -20 relative to gravitational strength.

  8. Diffeomorphic Iterative Centroid Methods for Template Estimation on Large Datasets

    OpenAIRE

    Cury , Claire; Glaunès , Joan Alexis; Colliot , Olivier

    2014-01-01

    International audience; A common approach for analysis of anatomical variability relies on the stimation of a template representative of the population. The Large Deformation Diffeomorphic Metric Mapping is an attractive framework for that purpose. However, template estimation using LDDMM is computationally expensive, which is a limitation for the study of large datasets. This paper presents an iterative method which quickly provides a centroid of the population in the shape space. This centr...

  9. Quantum W-algebras and elliptic algebras

    International Nuclear Information System (INIS)

    Feigin, B.; Kyoto Univ.; Frenkel, E.

    1996-01-01

    We define a quantum W-algebra associated to sl N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary W-algebra of sl N , or the q-deformed classical W-algebra of sl N . We construct free field realizations of the quantum W-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in U q (n). (orig.)

  10. Spontaneous Lorentz and diffeomorphism violation, massive modes, and gravity

    International Nuclear Information System (INIS)

    Bluhm, Robert; Fung Shuhong; Kostelecky, V. Alan

    2008-01-01

    Theories with spontaneous local Lorentz and diffeomorphism violation contain massless Nambu-Goldstone modes, which arise as field excitations in the minimum of the symmetry-breaking potential. If the shape of the potential also allows excitations above the minimum, then an alternative gravitational Higgs mechanism can occur in which massive modes involving the metric appear. The origin and basic properties of the massive modes are addressed in the general context involving an arbitrary tensor vacuum value. Special attention is given to the case of bumblebee models, which are gravitationally coupled vector theories with spontaneous local Lorentz and diffeomorphism violation. Mode expansions are presented in both local and spacetime frames, revealing the Nambu-Goldstone and massive modes via decomposition of the metric and bumblebee fields, and the associated symmetry properties and gauge fixing are discussed. The class of bumblebee models with kinetic terms of the Maxwell form is used as a focus for more detailed study. The nature of the associated conservation laws and the interpretation as a candidate alternative to Einstein-Maxwell theory are investigated. Explicit examples involving smooth and Lagrange-multiplier potentials are studied to illustrate features of the massive modes, including their origin, nature, dispersion laws, and effects on gravitational interactions. In the weak static limit, the massive mode and Lagrange-multiplier fields are found to modify the Newton and Coulomb potentials. The nature and implications of these modifications are examined.

  11. Rodrigues formulas for the non-symmetric multivariable polynomials associated with the BCN-type root system

    International Nuclear Information System (INIS)

    Nishino, Akinori; Ujino, Hideaki; Komori, Yasushi; Wadati, Miki

    2000-01-01

    The non-symmetric Macdonald-Koornwinder polynomials are joint eigenfunctions of the commuting Cherednik operators which are constructed from the representation theory for the affine Hecke algebra corresponding to the BC N -type root system. We present the Rodrigues formula for the non-symmetric Macdonald-Koornwinder polynomials. The raising operators are derived from the realizations of the corresponding double affine Hecke algebra. In the quasi-classical limit, the above theory reduces to that of the BC N -type Sutherland model which describes many particles with inverse-square long-range interactions on a circle with one impurity. We also present the Rodrigues formula for the non-symmetric Jacobi polynomials of type BC N which are eigenstates of the BC N -type Sutherland model

  12. Evaluation of GMI and PMI diffeomorphic-based demons algorithms for aligning PET and CT Images.

    Science.gov (United States)

    Yang, Juan; Wang, Hongjun; Zhang, You; Yin, Yong

    2015-07-08

    Fusion of anatomic information in computed tomography (CT) and functional information in 18F-FDG positron emission tomography (PET) is crucial for accurate differentiation of tumor from benign masses, designing radiotherapy treatment plan and staging of cancer. Although current PET and CT images can be acquired from combined 18F-FDG PET/CT scanner, the two acquisitions are scanned separately and take a long time, which may induce potential positional errors in global and local caused by respiratory motion or organ peristalsis. So registration (alignment) of whole-body PET and CT images is a prerequisite for their meaningful fusion. The purpose of this study was to assess the performance of two multimodal registration algorithms for aligning PET and CT images. The proposed gradient of mutual information (GMI)-based demons algorithm, which incorporated the GMI between two images as an external force to facilitate the alignment, was compared with the point-wise mutual information (PMI) diffeomorphic-based demons algorithm whose external force was modified by replacing the image intensity difference in diffeomorphic demons algorithm with the PMI to make it appropriate for multimodal image registration. Eight patients with esophageal cancer(s) were enrolled in this IRB-approved study. Whole-body PET and CT images were acquired from a combined 18F-FDG PET/CT scanner for each patient. The modified Hausdorff distance (d(MH)) was used to evaluate the registration accuracy of the two algorithms. Of all patients, the mean values and standard deviations (SDs) of d(MH) were 6.65 (± 1.90) voxels and 6.01 (± 1.90) after the GMI-based demons and the PMI diffeomorphic-based demons registration algorithms respectively. Preliminary results on oncological patients showed that the respiratory motion and organ peristalsis in PET/CT esophageal images could not be neglected, although a combined 18F-FDG PET/CT scanner was used for image acquisition. The PMI diffeomorphic-based demons

  13. Recoupling Lie algebra and universal ω-algebra

    International Nuclear Information System (INIS)

    Joyce, William P.

    2004-01-01

    We formulate the algebraic version of recoupling theory suitable for commutation quantization over any gradation. This gives a generalization of graded Lie algebra. Underlying this is the new notion of an ω-algebra defined in this paper. ω-algebra is a generalization of algebra that goes beyond nonassociativity. We construct the universal enveloping ω-algebra of recoupling Lie algebras and prove a generalized Poincare-Birkhoff-Witt theorem. As an example we consider the algebras over an arbitrary recoupling of Z n graded Heisenberg Lie algebra. Finally we uncover the usual coalgebra structure of a universal envelope and substantiate its Hopf structure

  14. Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra

    NARCIS (Netherlands)

    N.W. van den Hijligenberg; R. Martini

    1995-01-01

    textabstractWe discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra

  15. Enhancement in the Catalytic Activity of Pd/USY in the Heck Reaction Induced by H2 Bubbling

    Directory of Open Access Journals (Sweden)

    Miki Niwa

    2010-12-01

    Full Text Available Pd was loaded on ultra stable Y (USY zeolites prepared by steaming NH4-Y zeolite under different conditions. Heck reactions were carried out over the prepared Pd/USY. We found that H2 bubbling was effective in improving not only the catalytic activity of Pd/USY, but also that of other supported Pd catalysts and Pd(OAc2. Moreover, the catalytic activity of Pd/USY could be optimized by choosing appropriate steaming conditions for the preparation of the USY zeolites; Pd loaded on USY prepared at 873 K with 100% H2O gave the highest activity (TOF = 61,000 h−1, which was higher than that of Pd loaded on other kinds of supports. The prepared Pd/USY catalysts were applicable to the Heck reactions using various kinds of substrates including bromo- and chloro-substituted aromatic and heteroaromatic compounds. Characterization of the acid properties of the USY zeolites revealed that the strong acid site (OHstrong generated as a result of steaming had a profound effect on the catalytic activity of Pd.

  16. Enhancement in the catalytic activity of Pd/USY in the heck reaction induced by H2 bubbling.

    Science.gov (United States)

    Okumura, Kazu; Tomiyama, Takuya; Moriyama, Sayaka; Nakamichi, Ayaka; Niwa, Miki

    2010-12-24

    Pd was loaded on ultra stable Y (USY) zeolites prepared by steaming NH(4)-Y zeolite under different conditions. Heck reactions were carried out over the prepared Pd/USY. We found that H₂ bubbling was effective in improving not only the catalytic activity of Pd/USY, but also that of other supported Pd catalysts and Pd(OAc)₂. Moreover, the catalytic activity of Pd/USY could be optimized by choosing appropriate steaming conditions for the preparation of the USY zeolites; Pd loaded on USY prepared at 873 K with 100% H₂O gave the highest activity (TOF = 61,000 h⁻¹), which was higher than that of Pd loaded on other kinds of supports. The prepared Pd/USY catalysts were applicable to the Heck reactions using various kinds of substrates including bromo- and chloro-substituted aromatic and heteroaromatic compounds. Characterization of the acid properties of the USY zeolites revealed that the strong acid site (OH(strong)) generated as a result of steaming had a profound effect on the catalytic activity of Pd.

  17. The Yoneda algebra of a K2 algebra need not be another K2 algebra

    OpenAIRE

    Cassidy, T.; Phan, C.; Shelton, B.

    2010-01-01

    The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K2 algebra would be another K2 algebra. We show that this is not necessarily the case by constructing a monomial K2 algebra for which the corresponding Yoneda algebra is not K2.

  18. Gauge theories of infinite dimensional Hamiltonian superalgebras

    International Nuclear Information System (INIS)

    Sezgin, E.

    1989-05-01

    Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs

  19. Cylindric-like algebras and algebraic logic

    CERN Document Server

    Ferenczi, Miklós; Németi, István

    2013-01-01

    Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways:  as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.

  20. Quasi-local conserved charges in Lorenz-diffeomorphism covariant theory of gravity

    Energy Technology Data Exchange (ETDEWEB)

    Adami, H.; Setare, M.R. [University of Kurdistan, Department of Science, Sanandaj (Iran, Islamic Republic of)

    2016-04-15

    In this paper, using the combined Lorenz-diffeomorphism symmetry, we find a general formula for the quasi-local conserved charge of the covariant gravity theories in a first order formalism of gravity. We simplify the general formula for the Lovelock theory of gravity. Afterwards, we apply the obtained formula on BHT gravity to obtain the energy and angular momentum of the rotating OTT black hole solution in the context of this theory. (orig.)

  1. Quasi-local conserved charges in Lorenz-diffeomorphism covariant theory of gravity

    Science.gov (United States)

    Adami, H.; Setare, M. R.

    2016-04-01

    In this paper, using the combined Lorenz-diffeomorphism symmetry, we find a general formula for the quasi-local conserved charge of the covariant gravity theories in a first order formalism of gravity. We simplify the general formula for the Lovelock theory of gravity. Afterwards, we apply the obtained formula on BHT gravity to obtain the energy and angular momentum of the rotating OTT black hole solution in the context of this theory.

  2. Unusual selectivity-determining factors in the phosphine-free Heck arylation of allyl ethers

    DEFF Research Database (Denmark)

    Ambrogio, I.; Fabrizi, G.; Cacchi, S.

    2008-01-01

    The Heck reaction of aryl iodides and bromides with allyl ethers has been investigated. Using phosphinefree Pd(OAc)(2) in DNIF at 90 degrees C in the presence of Bu4NOAc, the reaction gave cinnamyl derivatives, usually in good to high yields, with a wide range of aryl halides. The reaction...... tolerates a variety of functional groups, including ether, amide, alcohol, aldehyde, ketone, ester, cyano, carboxylic acid, and nitro groups. Ortho-substituted arylating agents afforded moderate yields in some cases, though good to high yields were obtained with o-iodotoluene, iodovanillin, and 1...

  3. Diffeomorphism invariance in the Hamiltonian formulation of General Relativity

    International Nuclear Information System (INIS)

    Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.

    2008-01-01

    It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity

  4. Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra

    NARCIS (Netherlands)

    van den Hijligenberg, N.W.; van den Hijligenberg, N.W.; Martini, Ruud

    1995-01-01

    We discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of

  5. Fundamental structures of M(brane) theory

    International Nuclear Information System (INIS)

    Hoppe, Jens

    2011-01-01

    A dynamical symmetry, as well as special diffeomorphism algebras generalizing the Witt-Virasoro algebra, related to Poincare invariance and crucial with regard to quantization, questions of integrability, and M(atrix) theory, are found to exist in the theory of relativistic extended objects of any dimension.

  6. Constraining the break of spatial diffeomorphism invariance with Planck data

    Energy Technology Data Exchange (ETDEWEB)

    Graef, L.L.; Benetti, M.; Alcaniz, J.S., E-mail: leilagraef@on.br, E-mail: micolbenetti@on.br, E-mail: alcaniz@on.br [Departamento de Astronomia, Observatório Nacional, R. Gen. José Cristino, 77—São Cristóvão, 20921-400, Rio de Janeiro, RJ (Brazil)

    2017-07-01

    The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, which can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended ΛCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r , and the tensor spectral index, n {sub t} . If the inflation consistency relation is imposed, r =−8 n {sub t} , we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.

  7. Constraining the break of spatial diffeomorphism invariance with Planck data

    Science.gov (United States)

    Graef, L. L.; Benetti, M.; Alcaniz, J. S.

    2017-07-01

    The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, which can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended ΛCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r, and the tensor spectral index, nt. If the inflation consistency relation is imposed, r=-8 nt, we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.

  8. Introduction to relation algebras relation algebras

    CERN Document Server

    Givant, Steven

    2017-01-01

    The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly ...

  9. On the question of symmetries in nonrelativistic diffeomorphism-invariant theories

    Science.gov (United States)

    Banerjee, Rabin; Gangopadhyay, Sunandan; Mukherjee, Pradip

    2017-07-01

    A novel algorithm is provided to couple a Galilean-invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and canonical transformation of the original fields. That the twin requirements are fulfilled is ensured by a new field, the existence of which was demonstrated recently from Galilean gauge theory. The ambiguities and anomalies concerning the recovery of Galilean symmetry in the flat limit of spatial nonrelativistic diffeomorphic theories, reported in the literature, are focused and resolved from a new angle.

  10. From Rota-Baxter algebras to pre-Lie algebras

    International Nuclear Information System (INIS)

    An Huihui; Ba, Chengming

    2008-01-01

    Rota-Baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics. Rota-Baxter algebras provide a construction of pre-Lie algebras from associative algebras. In this paper, we give all Rota-Baxter operators of weight 1 on complex associative algebras in dimension ≤3 and their corresponding pre-Lie algebras

  11. Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

    International Nuclear Information System (INIS)

    Marquette, Ian

    2013-01-01

    We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently

  12. Quantum holonomy theory and Hilbert space representations

    Energy Technology Data Exchange (ETDEWEB)

    Aastrup, Johannes [Mathematisches Institut, Universitaet Hannover (Germany); Moeller Grimstrup, Jesper [QHT Gruppen, Copenhagen Area (Denmark)

    2016-11-15

    We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a Hilbert space representation of the QHD(M) algebra, which is generated by holonomy-diffeomorphisms on a 3-dimensional manifold and by canonical translation operators on the underlying configuration space over which the holonomy-diffeomorphisms form a non-commutative C*-algebra. A proof that the state that generates the representation exist is left for later publications. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  13. Yoneda algebras of almost Koszul algebras

    Indian Academy of Sciences (India)

    Abstract. Let k be an algebraically closed field, A a finite dimensional connected. (p,q)-Koszul self-injective algebra with p, q ≥ 2. In this paper, we prove that the. Yoneda algebra of A is isomorphic to a twisted polynomial algebra A![t; β] in one inde- terminate t of degree q +1 in which A! is the quadratic dual of A, β is an ...

  14. Time-dependent automorphism-inducing diffeomorphisms, open algebras and the generality of the Kantowski-Sachs vacuum geometry

    Science.gov (United States)

    Christodoulakis, T.; Papadopoulos, G. O.

    2002-10-01

    Following the spirit of a previous work of ours, we investigate the group of those general coordinate transformations (GCTs) which preserve manifest spatial homogeneity. In contrast to the case of Bianchi type models, here we permit an isometry group of motions G4 = SO(3) ⊗ Tr, where Tr is the translations group, along the radial direction, while SO(3) acts multiply transitively on each hypersurface of simultaneity Σt. The basis 1-forms cannot be invariant under the action of the entire isometry group and hence produce an open Lie algebra. In order for these GCTs to exist and have a nontrivial, well-defined action, certain integrability conditions have to be satisfied; their solutions, exhibiting the maximum expected 'gauge' freedom, can be used to simplify the generic, spatially homogeneous, line element. In this way an alternative proof of the generality of the Kantowski-Sachs (KS) vacuum is given, while its most general, manifestly homogeneous, form is explicitly presented.

  15. Quantum cluster algebras and quantum nilpotent algebras

    Science.gov (United States)

    Goodearl, Kenneth R.; Yakimov, Milen T.

    2014-01-01

    A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

  16. An introduction to algebraic geometry and algebraic groups

    CERN Document Server

    Geck, Meinolf

    2003-01-01

    An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups

  17. R-matrix and q-covariant oscillators for Uq(sl(n|m))

    International Nuclear Information System (INIS)

    Leblanc, Y.; Wallet, J.C.

    1993-02-01

    An R-matrix formalism is used to construct covariant quantum oscillator algebras for U q (sl(n|m)). It is shown that the complete structure of the twisted oscillator algebras can be obtained from the properties of the intertwining matrix obeying a Hecke type relation, combined with covariance of the oscillators at the deformed level and associativity. The resulting twisted algebras, involving q-bosons and q-fermions, are invariant under natural q-transformations of the oscillators induced by the coproduct. (author) 11 refs

  18. Multicomponent, flow diazotization/Mizoroki-Heck coupling protocol: dispelling myths about working with diazonium salts.

    Science.gov (United States)

    Nalivela, Kumara S; Tilley, Michael; McGuire, Michael A; Organ, Michael G

    2014-05-26

    A single pass flow diazotization/Mizoroki-Heck protocol has been developed for the production of cinnimoyl and styryl products. The factors that govern aryl diazonium salt stability have been examined in detail leading to the development of a MeOH/DMF co-solvent system in which the diazonium salts can be generated in the presence of all other reaction components and then coupled selectively to give the desired products. Finally the key role of the reaction quench for flow reactions has been demonstrated. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  19. Brandt matrices and theta series over global function fields

    CERN Document Server

    Chuang, Chih-Yun; Wei, Fu-Tsun; Yu, Jing

    2015-01-01

    The aim of this article is to give a complete account of the Eichler-Brandt theory over function fields and the basis problem for Drinfeld type automorphic forms. Given arbitrary function field k together with a fixed place \\infty, the authors construct a family of theta series from the norm forms of "definite" quaternion algebras, and establish an explicit Hecke-module homomorphism from the Picard group of an associated definite Shimura curve to a space of Drinfeld type automorphic forms. The "compatibility" of these homomorphisms with different square-free levels is also examined. These Heck

  20. Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra

    NARCIS (Netherlands)

    van den Hijligenberg, N.W.; van den Hijligenberg, N.; Martini, Ruud

    1995-01-01

    We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–Birkhoff–Witt type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebrastructure of U(g).

  1. The relation between quantum W algebras and Lie algebras

    International Nuclear Information System (INIS)

    Boer, J. de; Tjin, T.

    1994-01-01

    By quantizing the generalized Drinfeld-Sokolov reduction scheme for arbitrary sl 2 embeddings we show that a large set W of quantum W algebras can be viewed as (BRST) cohomologies of affine Lie algebras. The set W contains many known W algebras such as W N and W 3 (2) . Our formalism yields a completely algorithmic method for calculating the W algebra generators and their operator product expansions, replacing the cumbersome construction of W algebras as commutants of screening operators. By generalizing and quantizing the Miura transformation we show that any W algebra in W can be embedded into the universal enveloping algebra of a semisimple affine Lie algebra which is, up to shifts in level, isomorphic to a subalgebra of the original affine algebra. Therefore any realization of this semisimple affine Lie algebra leads to a realization of the W algebra. In particular, one obtains in this way a general and explicit method for constructing the free field realizations and Fock resolutions for all algebras in W. Some examples are explicitly worked out. (orig.)

  2. Reusable Polymer-Supported Terpyridine Palladium Complex for Suzuki-Miyaura, Mizoroki-Heck, Sonogashira, and Tsuji-Trost Reaction in Water

    Directory of Open Access Journals (Sweden)

    Takuya Nagamine

    2011-03-01

    Full Text Available A novel heterogeneous transition-metal catalyst comprising a polymer-supported terpyridine palladium(II complex was prepared and found to promote the Suzuki-Miyaura, Mizoroki-Heck, Sonogashira, and Tsuji-Trost, reactions in water under aerobic conditions with a high to excellent yield. The catalyst was recovered by simple filtration and directly reused several times without loss of catalytic activity.

  3. 2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras

    International Nuclear Information System (INIS)

    Ayupov, Shavkat; Kudaybergenov, Karimbergen

    2016-01-01

    The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2 n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation. (paper)

  4. Quantum cluster algebra structures on quantum nilpotent algebras

    CERN Document Server

    Goodearl, K R

    2017-01-01

    All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts.

  5. Constraint algebra in Smolin's G →0 limit of 4D Euclidean gravity

    Science.gov (United States)

    Varadarajan, Madhavan

    2018-05-01

    Smolin's generally covariant GNewton→0 limit of 4d Euclidean gravity is a useful toy model for the study of the constraint algebra in loop quantum gravity (LQG). In particular, the commutator between its Hamiltonian constraints has a metric dependent structure function. While a prior LQG-like construction of nontrivial anomaly free constraint commutators for the model exists, that work suffers from two defects. First, Smolin's remarks on the inability of the quantum dynamics to generate propagation effects apply. Second, the construction only yields the action of a single Hamiltonian constraint together with the action of its commutator through a continuum limit of corresponding discrete approximants; the continuum limit of a product of two or more constraints does not exist. Here, we incorporate changes in the quantum dynamics through structural modifications in the choice of discrete approximants to the quantum Hamiltonian constraint. The new structure is motivated by that responsible for propagation in an LQG-like quantization of paramatrized field theory and significantly alters the space of physical states. We study the off shell constraint algebra of the model in the context of these structural changes and show that the continuum limit action of multiple products of Hamiltonian constraints is (a) supported on an appropriate domain of states, (b) yields anomaly free commutators between pairs of Hamiltonian constraints, and (c) is diffeomorphism covariant. Many of our considerations seem robust enough to be applied to the setting of 4d Euclidean gravity.

  6. Quadratic algebras

    CERN Document Server

    Polishchuk, Alexander

    2005-01-01

    Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

  7. Regularity of C*-algebras and central sequence algebras

    DEFF Research Database (Denmark)

    Christensen, Martin S.

    The main topic of this thesis is regularity properties of C*-algebras and how these regularity properties are re ected in their associated central sequence algebras. The thesis consists of an introduction followed by four papers [A], [B], [C], [D]. In [A], we show that for the class of simple...... Villadsen algebra of either the rst type with seed space a nite dimensional CW complex, or the second type, tensorial absorption of the Jiang-Su algebra is characterized by the absence of characters on the central sequence algebra. Additionally, in a joint appendix with Joan Bosa, we show that the Villadsen...... algebra of the second type with innite stable rank fails the corona factorization property. In [B], we consider the class of separable C*-algebras which do not admit characters on their central sequence algebra, and show that it has nice permanence properties. We also introduce a new divisibility property...

  8. Real division algebras and other algebras motivated by physics

    International Nuclear Information System (INIS)

    Benkart, G.; Osborn, J.M.

    1981-01-01

    In this survey we discuss several general techniques which have been productive in the study of real division algebras, flexible Lie-admissible algebras, and other nonassociative algebras, and we summarize results obtained using these methods. The principal method involved in this work is to view an algebra A as a module for a semisimple Lie algebra of derivations of A and to use representation theory to study products in A. In the case of real division algebras, we also discuss the use of isotopy and the use of a generalized Peirce decomposition. Most of the work summarized here has appeared in more detail in various other papers. The exceptions are results on a class of algebras of dimension 15, motivated by physics, which admit the Lie algebra sl(3) as an algebra of derivations

  9. Hom-Novikov algebras

    International Nuclear Information System (INIS)

    Yau, Donald

    2011-01-01

    We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions 2 or 3 are computed, and their associated Hom-Novikov algebras are described explicitly. Another class of Hom-Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom-Novikov algebras are constructed from Hom-Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.

  10. Linear algebra meets Lie algebra: the Kostant-Wallach theory

    OpenAIRE

    Shomron, Noam; Parlett, Beresford N.

    2008-01-01

    In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.

  11. An application of the division algebras, Jordan algebras and split composition algebras

    International Nuclear Information System (INIS)

    Foot, R.; Joshi, G.C.

    1992-01-01

    It has been established that the covering group of the Lorentz group in D = 3, 4, 6, 10 can be expressed in a unified way, based on the four composition division algebras R, C, Q and O. In this paper, the authors discuss, in this framework, the role of the complex numbers of quantum mechanics. A unified treatment of quantum-mechanical spinors is given. The authors provide an explicit demonstration that the vector and spinor transformations recently constructed from a subgroup of the reduced structure group of the Jordan algebras M n 3 are indeed the Lorentz transformations. The authors also show that if the division algebras in the construction of the covering groups of the Lorentz groups in D = 3, 4, 6, 10 are replaced by the split composition algebras, then the sequence of groups SO(2, 2), SO(3, 3) and SO(5, 5) result. The analysis is presumed to be self-contained as the relevant aspects of the division algebras and Jordan algebras are reviewed. Some applications to physical theory are indicated

  12. Interactions Between Representation Ttheory, Algebraic Topology and Commutative Algebra

    CERN Document Server

    Pitsch, Wolfgang; Zarzuela, Santiago

    2016-01-01

    This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest dev...

  13. Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

    Science.gov (United States)

    Verburgt, Lukas M

    2016-01-01

    This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.

  14. Palladium(II/Cationic 2,2’-Bipyridyl System as a Highly Efficient and Reusable Catalyst for the Mizoroki-Heck Reaction in Water

    Directory of Open Access Journals (Sweden)

    Fu-Yu Tsai

    2010-01-01

    Full Text Available A water-soluble and air-stable Pd(NH32Cl2/cationic 2,2’-bipyridyl system was found to be a highly-efficient and reusable catalyst for the coupling of aryl iodides and alkenes in neat water using Bu3N as a base. The reaction was conducted at 140 °C in a sealed tube in air with a catalyst loading as low as 0.0001 mol % for the coupling of activated aryl iodides with butyl and ethyl acrylates, providing the corresponding products in good to excellent yields with very high turnover numbers. In the case of styrene, Mizoroki-Heck coupling products were obtained in good to high yields by using a greater catalyst loading (1 mol % and TBAB as a phase-transfer agent. After extraction, the residual aqueous solution could be reused several times with only a slight decrease in its activity, making the Mizoroki-Heck reaction “greener”.

  15. Monomial algebras

    CERN Document Server

    Villarreal, Rafael

    2015-01-01

    The book stresses the interplay between several areas of pure and applied mathematics, emphasizing the central role of monomial algebras. It unifies the classical results of commutative algebra with central results and notions from graph theory, combinatorics, linear algebra, integer programming, and combinatorial optimization. The book introduces various methods to study monomial algebras and their presentation ideals, including Stanley-Reisner rings, subrings and blowup algebra-emphasizing square free quadratics, hypergraph clutters, and effective computational methods.

  16. Algebra

    CERN Document Server

    Tabak, John

    2004-01-01

    Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries, and offers biographical data on the key figures. Concise and comprehensive text accompanied by many illustrations presents the ideas and historical development of algebra, showcasing the relevance and evolution of this branch of mathematics.

  17. Algebra of pseudo-differential operators over C*-algebra

    International Nuclear Information System (INIS)

    Mohammad, N.

    1982-08-01

    Algebras of pseudo-differential operators over C*-algebras are studied for the special case when in Hormander class Ssub(rho,delta)sup(m)(Ω) Ω = Rsup(n); rho = 1, delta = 0, m any real number, and the C*-algebra is infinite dimensional non-commutative. The space B, i.e. the set of A-valued C*-functions in Rsup(n) (or Rsup(n) x Rsup(n)) whose derivatives are all bounded, plays an important role. A denotes C*-algebra. First the operator class Ssub(phi,0)sup(m) is defined, and through it, the class Lsub(1,0)sup(m) of pseudo-differential operators. Then the basic asymptotic expansion theorems concerning adjoint and product of operators of class Ssub(1,0)sup(m) are stated. Finally, proofs are given of L 2 -continuity theorem and the main theorem, which states that algebra of all pseudo-differential operators over C*-algebras is itself C*-algebra

  18. Commutative algebra with a view toward algebraic geometry

    CERN Document Server

    Eisenbud, David

    1995-01-01

    Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algeb...

  19. Jordan algebras versus C*- algebras

    International Nuclear Information System (INIS)

    Stormer, E.

    1976-01-01

    The axiomatic formulation of quantum mechanics and the problem of whether the observables form self-adjoint operators on a Hilbert space, are discussed. The relation between C*- algebras and Jordan algebras is studied using spectral theory. (P.D.)

  20. Implicative Algebras

    African Journals Online (AJOL)

    Tadesse

    In this paper we introduce the concept of implicative algebras which is an equivalent definition of lattice implication algebra of Xu (1993) and further we prove that it is a regular Autometrized. Algebra. Further we remark that the binary operation → on lattice implicative algebra can never be associative. Key words: Implicative ...

  1. Open algebraic surfaces

    CERN Document Server

    Miyanishi, Masayoshi

    2000-01-01

    Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods to study the geometry and topology of open algebraic surfaces. The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities. This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces. Prerequisite to understanding the text is a basic b...

  2. Separable algebras

    CERN Document Server

    Ford, Timothy J

    2017-01-01

    This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.

  3. Does there exist a sensible quantum theory of an ''algebra-valued'' scalar field?

    International Nuclear Information System (INIS)

    Anco, S.C.; Wald, R.M.

    1989-01-01

    Consider a scalar field phi in Minkowski spacetime, but let phi be valued in an associative, commutative algebra openA rather than openR. One may view the resulting theory as describing a collection of coupled real scalar fields. At the classical level, theories of this type are completely well behaved and have a global symmetry group which is a nontrivial enlargement of the Poincare group. (They are analogs of the new class of gauge theories for massless spin-2 fields found recently by one of us, whose gauge group is a nontrivial enlargement of the usual diffeomorphism group.) We investigate the quantization of such scalar field theories here by studying the case of a λphi 4 field, with phi valued in the two-dimensional algebra generated by an identity element e and a nilpotent element v satisfying v 2 = 0. The Coleman-Mandula theorem, which states that the symmetry group of a nontrivial quantum field theory cannot be a nontrivial enlargement of the Poincare group, is evaded here because the finite ''extra'' symmetries of the classical theory fail to be implemented in the quantum theory by unitary operators and the infinitesimal symmetries (which can be represented in the quantum theory by quadratic forms) connect the one-particle Hilbert space to multiparticle states. Nevertheless, we find that the conventional Feynman rules for this theory lead to vacuum decay at the tree level and fail to yield a well-defined S matrix. Some alternative approaches are investigated, but these also appear to fail

  4. Generalized EMV-Effect Algebras

    Science.gov (United States)

    Borzooei, R. A.; Dvurečenskij, A.; Sharafi, A. H.

    2018-04-01

    Recently in Dvurečenskij and Zahiri (2017), new algebraic structures, called EMV-algebras which generalize both MV-algebras and generalized Boolean algebras, were introduced. We present equivalent conditions for EMV-algebras. In addition, we define a partial algebraic structure, called a generalized EMV-effect algebra, which is close to generalized MV-effect algebras. Finally, we show that every generalized EMV-effect algebra is either an MV-effect algebra or can be embedded into an MV-effect algebra as a maximal ideal.

  5. Special set linear algebra and special set fuzzy linear algebra

    OpenAIRE

    Kandasamy, W. B. Vasantha; Smarandache, Florentin; Ilanthenral, K.

    2009-01-01

    The authors in this book introduce the notion of special set linear algebra and special set fuzzy Linear algebra, which is an extension of the notion set linear algebra and set fuzzy linear algebra. These concepts are best suited in the application of multi expert models and cryptology. This book has five chapters. In chapter one the basic concepts about set linear algebra is given in order to make this book a self contained one. The notion of special set linear algebra and their fuzzy analog...

  6. Banach Synaptic Algebras

    Science.gov (United States)

    Foulis, David J.; Pulmannov, Sylvia

    2018-04-01

    Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

  7. Grassmann algebras

    International Nuclear Information System (INIS)

    Garcia, R.L.

    1983-11-01

    The Grassmann algebra is presented briefly. Exponential and logarithm of matrices functions, whose elements belong to this algebra, are studied with the help of the SCHOONSCHIP and REDUCE 2 algebraic manipulators. (Author) [pt

  8. Algebraic geometry

    CERN Document Server

    Lefschetz, Solomon

    2005-01-01

    An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

  9. Converting nested algebra expressions into flat algebra expressions

    NARCIS (Netherlands)

    Paredaens, J.; Van Gucht, D.

    1992-01-01

    Nested relations generalize ordinary flat relations by allowing tuple values to be either atomic or set valued. The nested algebra is a generalization of the flat relational algebra to manipulate nested relations. In this paper we study the expressive power of the nested algebra relative to its

  10. Fibered F-Algebra

    OpenAIRE

    Kleyn, Aleks

    2007-01-01

    The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of representation of F-algebra and of representation of fibered F-algebra.

  11. The bubble algebra: structure of a two-colour Temperley-Lieb Algebra

    International Nuclear Information System (INIS)

    Grimm, Uwe; Martin, Paul P

    2003-01-01

    We define new diagram algebras providing a sequence of multiparameter generalizations of the Temperley-Lieb algebra, suitable for the modelling of dilute lattice systems of two-dimensional statistical mechanics. These algebras give a rigorous foundation to the various 'multi-colour algebras' of Grimm, Pearce and others. We determine the generic representation theory of the simplest of these algebras, and locate the nongeneric cases (at roots of unity of the corresponding parameters). We show by this example how the method used (Martin's general procedure for diagram algebras) may be applied to a wide variety of such algebras occurring in statistical mechanics. We demonstrate how these algebras may be used to solve the Yang-Baxter equations

  12. Hamiltonian constraint in polymer parametrized field theory

    International Nuclear Information System (INIS)

    Laddha, Alok; Varadarajan, Madhavan

    2011-01-01

    Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.

  13. DFT-Based Explanation of the Effect of Simple Anionic Ligands on the Regioselectivity of the Heck Arylation of Acrolein Acetals

    DEFF Research Database (Denmark)

    Henriksen, Signe Teuber; Tanner, David Ackland; Cacchi, Sandro

    2009-01-01

    The Heck arylation of acrolein acetal has been studied computationally and compared to the corresponding reaction with allyl ethers. The reaction can be controlled to give either cinnamaldehydes or arylpropanoic esters by addition of different coordinating anions, acetate, or chloride. The comput...... reaction conditions. The difference between the two substrate classes could be rationalized in terms of relative hydride donating power of the two substrates....

  14. Algebraic monoids, group embeddings, and algebraic combinatorics

    CERN Document Server

    Li, Zhenheng; Steinberg, Benjamin; Wang, Qiang

    2014-01-01

    This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.   Topics presented include:   v  structure and representation theory of reductive algebraic monoids v  monoid schemes and applications of monoids v  monoids related to Lie theory v  equivariant embeddings of algebraic groups v  constructions and properties of monoids from algebraic combinatorics v  endomorphism monoids induced from vector bundles v  Hodge–Newton decompositions of reductive monoids   A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semigroups are strongly π-regular.   Graduate students as well a...

  15. Leavitt path algebras

    CERN Document Server

    Abrams, Gene; Siles Molina, Mercedes

    2017-01-01

    This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and...

  16. Approximation of complex algebraic numbers by algebraic numbers of bounded degree

    OpenAIRE

    Bugeaud, Yann; Evertse, Jan-Hendrik

    2007-01-01

    We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It follows from our investigations that for every positive integer n there are complex algebraic numbers of degree larger than n that are better approximable by algebraic numbers of degree at most n than almost all complex numbers. As it turns out, these numbers ar...

  17. Operadic formulation of topological vertex algebras and gerstenhaber or Batalin-Vilkovisky algebras

    International Nuclear Information System (INIS)

    Huang Yizhi

    1994-01-01

    We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak topological vertex algebra) by combining this operadic formulation with a theorem of Getzler (or of Cohen) which formulates Batalin-Vilkovisky algebras (or Gerstenhaber algebras) in terms of the homology of the framed little disk operad (or of the little disk operad). (orig.)

  18. Wn(2) algebras

    International Nuclear Information System (INIS)

    Feigin, B.L.; Semikhatov, A.M.

    2004-01-01

    We construct W-algebra generalizations of the sl-circumflex(2) algebra-W algebras W n (2) generated by two currents E and F with the highest pole of order n in their OPE. The n=3 term in this series is the Bershadsky-Polyakov W 3 (2) algebra. We define these algebras as a centralizer (commutant) of the Uqs-bar (n vertical bar 1) quantum supergroup and explicitly find the generators in a factored, 'Miura-like' form. Another construction of the W n (2) algebras is in terms of the coset sl-circumflex(n vertical bar 1)/sl-circumflex(n). The relation between the two constructions involves the 'duality' (k+n-1)(k'+n-1)=1 between levels k and k' of two sl-circumflex(n) algebras

  19. The vacuum preserving Lie algebra of a classical W-algebra

    International Nuclear Information System (INIS)

    Feher, L.; Tsutsui, I.

    1993-07-01

    We simplify and generalize an argument due to Bowcock and Watts showing that one can associate a finite Lie algebra (the 'classical vacuum preserving algebra') containing the Moebius sl(2) subalgebra to any classical W-algebra. Our construction is based on a kinematical analysis of the Poisson brackets of quasi-fields. In the case of the W S G -subalgebra S of a simple Lie algebra G, we exhibit a natural isomorphism between this finite Lie algebra and G whereby the Moebius sl(2) is identified with S. (orig.)

  20. Nonflexible Lie-admissible algebras

    International Nuclear Information System (INIS)

    Myung, H.C.

    1978-01-01

    We discuss the structure of Lie-admissible algebras which are defined by nonflexible identities. These algebras largely arise from the antiflexible algebras, 2-varieties and associator dependent algebras. The nonflexible Lie-admissible algebras in our discussion are in essence byproducts of the study of nonassociative algebras defined by identities of degree 3. The main purpose is to discuss the classification of simple Lie-admissible algebras of nonflexible type

  1. On 2-Banach algebras

    International Nuclear Information System (INIS)

    Mohammad, N.; Siddiqui, A.H.

    1987-11-01

    The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor product, several classical results of Banach algebras are extended to the 2-Banach algebra case. A condition under which a 2-Banach algebra becomes a Banach algebra is obtained and the relation between algebra of bivectors and 2-normed algebra is discussed. 11 refs

  2. Algebra

    CERN Document Server

    Flanders, Harley

    1975-01-01

    Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms.Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of a

  3. Lukasiewicz-Moisil algebras

    CERN Document Server

    Boicescu, V; Georgescu, G; Rudeanu, S

    1991-01-01

    The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation.Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.

  4. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    Science.gov (United States)

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  5. The Boolean algebra and central Galois algebras

    Directory of Open Access Journals (Sweden)

    George Szeto

    2001-01-01

    Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B∣bx=g(xb   for all   x∈B} for g∈G, and BJg=Beg for a central idempotent eg. Then a relation is given between the set of elements in the Boolean algebra (Ba,≤ generated by {0,eg∣g∈G} and a set of subgroups of G, and a central Galois algebra Be with a Galois subgroup of G is characterized for an e∈Ba.

  6. Wavelets and quantum algebras

    International Nuclear Information System (INIS)

    Ludu, A.; Greiner, M.

    1995-09-01

    A non-linear associative algebra is realized in terms of translation and dilation operators, and a wavelet structure generating algebra is obtained. We show that this algebra is a q-deformation of the Fourier series generating algebra, and reduces to this for certain value of the deformation parameter. This algebra is also homeomorphic with the q-deformed su q (2) algebra and some of its extensions. Through this algebraic approach new methods for obtaining the wavelets are introduced. (author). 20 refs

  7. Novikov-Jordan algebras

    OpenAIRE

    Dzhumadil'daev, A. S.

    2002-01-01

    Algebras with identity $(a\\star b)\\star (c\\star d) -(a\\star d)\\star(c\\star b)$ $=(a,b,c)\\star d-(a,d,c)\\star b$ are studied. Novikov algebras under Jordan multiplication and Leibniz dual algebras satisfy this identity. If algebra with such identity has unit, then it is associative and commutative.

  8. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    Science.gov (United States)

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  9. Scope and limitations of the Heck-Matsuda-coupling of phenol diazonium salts and styrenes: a protecting-group economic synthesis of phenolic stilbenes.

    Science.gov (United States)

    Schmidt, Bernd; Elizarov, Nelli; Berger, René; Hölter, Frank

    2013-06-14

    4-Phenol diazonium salts undergo Pd-catalyzed Heck reactions with various styrenes to 4'-hydroxy stilbenes. In almost all cases higher yields and fewer side products were observed, compared to the analogous 4-methoxy benzene diazonium salts. In contrast, the reaction fails completely with 2- and 3-phenol diazonium salts. For these substitution patterns the methoxy-substituted derivatives are superior.

  10. (Quasi-)Poisson enveloping algebras

    OpenAIRE

    Yang, Yan-Hong; Yao, Yuan; Ye, Yu

    2010-01-01

    We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.

  11. Iterated Leavitt Path Algebras

    International Nuclear Information System (INIS)

    Hazrat, R.

    2009-11-01

    Leavitt path algebras associate to directed graphs a Z-graded algebra and in their simplest form recover the Leavitt algebras L(1,k). In this note, we introduce iterated Leavitt path algebras associated to directed weighted graphs which have natural ± Z grading and in their simplest form recover the Leavitt algebras L(n,k). We also characterize Leavitt path algebras which are strongly graded. (author)

  12. Algebraic topological entropy

    International Nuclear Information System (INIS)

    Hudetz, T.

    1989-01-01

    As a 'by-product' of the Connes-Narnhofer-Thirring theory of dynamical entropy for (originally non-Abelian) nuclear C * -algebras, the well-known variational principle for topological entropy is eqivalently reformulated in purly algebraically defined terms for (separable) Abelian C * -algebras. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle (at least 'in principle'). 23 refs. (Author)

  13. Linearizing W-algebras

    International Nuclear Information System (INIS)

    Krivonos, S.O.; Sorin, A.S.

    1994-06-01

    We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras W 3 and W (2) 3 can be embedded as subalgebras into some linear algebras with finite set of currents. Using these linear algebras we find new field realizations of W (2) 3 and W 3 which could be a starting point for constructing new versions of W-string theories. We also reveal a number of hidden relationships between W 3 and W (2) 3 . We conjecture that similar linear algebras can exist for other W-algebra as well. (author). 10 refs

  14. S-HAMMER: hierarchical attribute-guided, symmetric diffeomorphic registration for MR brain images.

    Science.gov (United States)

    Wu, Guorong; Kim, Minjeong; Wang, Qian; Shen, Dinggang

    2014-03-01

    Deformable registration has been widely used in neuroscience studies for spatial normalization of brain images onto the standard space. Because of possible large anatomical differences across different individual brains, registration performance could be limited when trying to estimate a single directed deformation pathway, i.e., either from template to subject or from subject to template. Symmetric image registration, however, offers an effective way to simultaneously deform template and subject images toward each other until they meet at the middle point. Although some intensity-based registration algorithms have nicely incorporated this concept of symmetric deformation, the pointwise intensity matching between two images may not necessarily imply the matching of correct anatomical correspondences. Based on HAMMER registration algorithm (Shen and Davatzikos, [2002]: IEEE Trans Med Imaging 21:1421-1439), we integrate the strategies of hierarchical attribute matching and symmetric diffeomorphic deformation to build a new symmetric-diffeomorphic HAMMER registration algorithm, called as S-HAMMER. The performance of S-HAMMER has been extensively compared with 14 state-of-the-art nonrigid registration algorithms evaluated in (Klein et al., [2009]: NeuroImage 46:786-802) by using real brain images in LPBA40, IBSR18, CUMC12, and MGH10 datasets. In addition, the registration performance of S-HAMMER, by comparison with other methods, is also demonstrated on both elderly MR brain images (>70 years old) and the simulated brain images with ground-truth deformation fields. In all experiments, our proposed method achieves the best registration performance over all other registration methods, indicating the high applicability of our method in future neuroscience and clinical applications. Copyright © 2013 Wiley Periodicals, Inc.

  15. Quantum deformed su(mvertical stroke n) algebra and superconformal algebra on quantum superspace

    International Nuclear Information System (INIS)

    Kobayashi, Tatsuo

    1993-01-01

    We study a deformed su(mvertical stroke n) algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. From the deformed su(1vertical stroke 4) algebra, we derive deformed Lorentz, translation of Minkowski space, iso(2,2) and its supersymmetric algebras as closed subalgebras with consistent automorphisms. (orig.)

  16. Linear algebraic groups

    CERN Document Server

    Springer, T A

    1998-01-01

    "[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text." –Mathematical Reviews (Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of t...

  17. Extended conformal algebras

    International Nuclear Information System (INIS)

    Goddard, Peter

    1990-01-01

    The algebra of the group of conformal transformations in two dimensions consists of two commuting copies of the Virasoro algebra. In many mathematical and physical contexts, the representations of ν which are relevant satisfy two conditions: they are unitary and they have the ''positive energy'' property that L o is bounded below. In an irreducible unitary representation the central element c takes a fixed real value. In physical contexts, the value of c is a characteristic of a theory. If c < 1, it turns out that the conformal algebra is sufficient to ''solve'' the theory, in the sense of relating the calculation of the infinite set of physically interesting quantities to a finite subset which can be handled in principle. For c ≥ 1, this is no longer the case for the algebra alone and one needs some sort of extended conformal algebra, such as the superconformal algebra. It is these algebras that this paper aims at addressing. (author)

  18. Generalized symmetry algebras

    International Nuclear Information System (INIS)

    Dragon, N.

    1979-01-01

    The possible use of trilinear algebras as symmetry algebras for para-Fermi fields is investigated. The shortcomings of the examples are argued to be a general feature of such generalized algebras. (author)

  19. Continuous-flow Heck synthesis of 4-methoxybiphenyl and methyl 4-methoxycinnamate in supercritical carbon dioxide expanded solvent solutions

    Directory of Open Access Journals (Sweden)

    Phei Li Lau

    2013-12-01

    Full Text Available The palladium metal catalysed Heck reaction of 4-iodoanisole with styrene or methyl acrylate has been studied in a continuous plug flow reactor (PFR using supercritical carbon dioxide (scCO2 as the solvent, with THF and methanol as modifiers. The catalyst was 2% palladium on silica and the base was diisopropylethylamine due to its solubility in the reaction solvent. No phosphine co-catalysts were used so the work-up procedure was simplified and the green credentials of the reaction were enhanced. The reactions were studied as a function of temperature, pressure and flow rate and in the case of the reaction with styrene compared against a standard, stirred autoclave reaction. Conversion was determined and, in the case of the reaction with styrene, the isomeric product distribution was monitored by GC. In the case of the reaction with methyl acrylate the reactor was scaled from a 1.0 mm to 3.9 mm internal diameter and the conversion and turnover frequency determined. The results show that the Heck reaction can be effectively performed in scCO2 under continuous flow conditions with a palladium metal, phosphine-free catalyst, but care must be taken when selecting the reaction temperature in order to ensure the appropriate isomer distribution is achieved. Higher reaction temperatures were found to enhance formation of the branched terminal alkene isomer as opposed to the linear trans-isomer.

  20. Rota-Baxter algebras and the Hopf algebra of renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Ebrahimi-Fard, K.

    2006-06-15

    Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

  1. Rota-Baxter algebras and the Hopf algebra of renormalization

    International Nuclear Information System (INIS)

    Ebrahimi-Fard, K.

    2006-06-01

    Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

  2. Galilean contractions of W-algebras

    Directory of Open Access Journals (Sweden)

    Jørgen Rasmussen

    2017-09-01

    Full Text Available Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as W-algebras. Known examples include contractions of pairs of the Virasoro algebra, its N=1 superconformal extension, or the W3 algebra. Here, we introduce a contraction prescription of the corresponding operator-product algebras, or equivalently, a prescription for contracting tensor products of vertex algebras. With this, we work out the Galilean conformal algebras arising from contractions of N=2 and N=4 superconformal algebras as well as of the W-algebras W(2,4, W(2,6, W4, and W5. The latter results provide evidence for the existence of a whole new class of W-algebras which we call Galilean W-algebras. We also apply the contraction prescription to affine Lie algebras and find that the ensuing Galilean affine algebras admit a Sugawara construction. The corresponding central charge is level-independent and given by twice the dimension of the underlying finite-dimensional Lie algebra. Finally, applications of our results to the characterisation of structure constants in W-algebras are proposed.

  3. Quantum affine algebras and deformations of the virasoro and W-algebras

    International Nuclear Information System (INIS)

    Frenkel, E.; Reshetikhin, N.

    1996-01-01

    Using the Wakimoto realization of quantum affine algebras we define new Poisson algebras, which are q-deformations of the classical W-algebras. We also define their free field realizations, i.e. homomorphisms into some Heisenberg-Poisson algebras. The formulas for these homomorphisms coincide with formulas for spectra of transfer-matrices in the corresponding quantum integrable models derived by the Bethe-Ansatz method. (orig.)

  4. Algebraic entropy for algebraic maps

    International Nuclear Information System (INIS)

    Hone, A N W; Ragnisco, Orlando; Zullo, Federico

    2016-01-01

    We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations. (letter)

  5. On hyper BCC-algebras

    OpenAIRE

    Borzooei, R. A.; Dudek, W. A.; Koohestani, N.

    2006-01-01

    We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.

  6. Symmetric functions and orthogonal polynomials

    CERN Document Server

    Macdonald, I G

    1997-01-01

    One of the most classical areas of algebra, the theory of symmetric functions and orthogonal polynomials has long been known to be connected to combinatorics, representation theory, and other branches of mathematics. Written by perhaps the most famous author on the topic, this volume explains some of the current developments regarding these connections. It is based on lectures presented by the author at Rutgers University. Specifically, he gives recent results on orthogonal polynomials associated with affine Hecke algebras, surveying the proofs of certain famous combinatorial conjectures.

  7. A new deformation of W-infinity and applications to the two-loop WZNW and conformal affine Toda models

    International Nuclear Information System (INIS)

    Aratyn, H.; Ferreira, L.A.; Gomes, J.F.; Zimerman, A.H.

    1992-01-01

    We constructed a center less W-infinity type of algebra in terms of a generator of a center less Virasoro algebra and an Abelian spin-1 current. This algebra conventionally emerges in the study of pseudo-differential operators on a circle or alternatively within KP hierarchy with Watanabe's bracket. Construction used here is based on a special deformation of the algebra w ∞ of area preserving diffeomorphisms of a 2-manifold. We show that this deformation technique applies to the two-loop WZNW and conformal affine Toda models, establishing henceforth W ∞ invariance of these models. (author)

  8. On hyper BCC-algebras

    Directory of Open Access Journals (Sweden)

    R. A. Borzooei

    2006-01-01

    Full Text Available We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.

  9. Algebraic theory of numbers

    CERN Document Server

    Samuel, Pierre

    2008-01-01

    Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal

  10. The BRS algebra of a free differential algebra

    International Nuclear Information System (INIS)

    Boukraa, S.

    1987-04-01

    We construct in this work, the Weil and the universal BRS algebras of theories that can have as a gauge symmetry a free differential (Sullivan) algebra, the natural extension of Lie algebras allowing the definition of p-form gauge potentials (p>1). The finite gauge transformations of these potentials are deduced from the infinitesimal ones and the group structure is shown. The geometrical meaning of these p-form gauge potentials is given by the notion of a Quillen superconnection. (author). 19 refs

  11. Metodologies d’anulació en substrats heterocíclics: Reaccions de RCM i ciclacions de Heck

    OpenAIRE

    Alonso Serrano, Sandra

    2010-01-01

    [cat] La present Tesi Doctoral es situa en el context de l’estudi d’estratègies sintètiques per a la formació d’anells en l’àrea heterocíclica. En particular, s’han avaluat les possibilitats sintètiques de la combinació de dues reaccions d’eficàcia prou reconeguda per a la formació d’enllaços carboni-carboni, la reacció de RCM i la reacció intramolecular de Heck d’halurs vinílics, per a la construcció de les estructures policíliques amb pont característiques dels alcaloides ervitsina i apari...

  12. Pseudo-Riemannian Novikov algebras

    Energy Technology Data Exchange (ETDEWEB)

    Chen Zhiqi; Zhu Fuhai [School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 (China)], E-mail: chenzhiqi@nankai.edu.cn, E-mail: zhufuhai@nankai.edu.cn

    2008-08-08

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.

  13. On the PR-algebras

    International Nuclear Information System (INIS)

    Lebedenko, V.M.

    1978-01-01

    The PR-algebras, i.e. the Lie algebras with commutation relations of [Hsub(i),Hsub(j)]=rsub(ij)Hsub(i)(i< j) type are investigated. On the basis of former results a criterion for the membership of 2-solvable Lie algebras to the PR-algebra class is given. The conditions imposed by the criterion are formulated in the linear algebra language

  14. Introduction to W-algebras

    International Nuclear Information System (INIS)

    Takao, Masaru

    1989-01-01

    We review W-algebras which are generated by stress tensor and primary fields. Associativity plays an important role in determining the extended algebra and further implies the algebras to exist for special values of central charges. Explicitly constructing the algebras including primary fields of spin less than 4, we investigate the closure structure of the Jacobi identity of the extended algebras. (author)

  15. (Modular Effect Algebras are Equivalent to (Frobenius Antispecial Algebras

    Directory of Open Access Journals (Sweden)

    Dusko Pavlovic

    2017-01-01

    Full Text Available Effect algebras are one of the generalizations of Boolean algebras proposed in the quest for a quantum logic. Frobenius algebras are a tool of categorical quantum mechanics, used to present various families of observables in abstract, often nonstandard frameworks. Both effect algebras and Frobenius algebras capture their respective fragments of quantum mechanics by elegant and succinct axioms; and both come with their conceptual mysteries. A particularly elegant and mysterious constraint, imposed on Frobenius algebras to characterize a class of tripartite entangled states, is the antispecial law. A particularly contentious issue on the quantum logic side is the modularity law, proposed by von Neumann to mitigate the failure of distributivity of quantum logical connectives. We show that, if quantum logic and categorical quantum mechanics are formalized in the same framework, then the antispecial law of categorical quantum mechanics corresponds to the natural requirement of effect algebras that the units are each other's unique complements; and that the modularity law corresponds to the Frobenius condition. These correspondences lead to the equivalence announced in the title. Aligning the two formalisms, at the very least, sheds new light on the concepts that are more clearly displayed on one side than on the other (such as e.g. the orthogonality. Beyond that, it may also open up new approaches to deep and important problems of quantum mechanics (such as the classification of complementary observables.

  16. An algorithm to construct the basic algebra of a skew group algebra

    NARCIS (Netherlands)

    Horobeţ, E.

    2016-01-01

    We give an algorithm for the computation of the basic algebra Morita equivalent to a skew group algebra of a path algebra by obtaining formulas for the number of vertices and arrows of the new quiver Qb. We apply this algorithm to compute the basic algebra corresponding to all simple quaternion

  17. Compact quantum group C*-algebras as Hopf algebras with approximate unit

    International Nuclear Information System (INIS)

    Do Ngoc Diep; Phung Ho Hai; Kuku, A.O.

    1999-04-01

    In this paper, we construct and study the representation theory of a Hopf C*-algebra with approximate unit, which constitutes quantum analogue of a compact group C*-algebra. The construction is done by first introducing a convolution-product on an arbitrary Hopf algebra H with integral, and then constructing the L 2 and C*-envelopes of H (with the new convolution-product) when H is a compact Hopf *-algebra. (author)

  18. Intervals in Generalized Effect Algebras and their Sub-generalized Effect Algebras

    Directory of Open Access Journals (Sweden)

    Zdenka Riečanová

    2013-01-01

    Full Text Available We consider subsets G of a generalized effect algebra E with 0∈G and such that every interval [0, q]G = [0, q]E ∩ G of G (q ∈ G , q ≠ 0 is a sub-effect algebra of the effect algebra [0, q]E. We give a condition on E and G under which every such G is a sub-generalized effect algebra of E.

  19. Variants of bosonization in parabosonic algebra: the Hopf and super-Hopf structures in parabosonic algebra

    International Nuclear Information System (INIS)

    Kanakoglou, K; Daskaloyannis, C

    2008-01-01

    Parabosonic algebra in finite or infinite degrees of freedom is considered as a Z 2 -graded associative algebra, and is shown to be a Z 2 -graded (or super) Hopf algebra. The super-Hopf algebraic structure of the parabosonic algebra is established directly without appealing to its relation to the osp(1/2n) Lie superalgebraic structure. The notion of super-Hopf algebra is equivalently described as a Hopf algebra in the braided monoidal category CZ 2 M. The bosonization technique for switching a Hopf algebra in the braided monoidal category H M (where H is a quasitriangular Hopf algebra) into an ordinary Hopf algebra is reviewed. In this paper, we prove that for the parabosonic algebra P B , beyond the application of the bosonization technique to the original super-Hopf algebra, a bosonization-like construction is also achieved using two operators, related to the parabosonic total number operator. Both techniques switch the same super-Hopf algebra P B to an ordinary Hopf algebra, thus producing two different variants of P B , with an ordinary Hopf structure

  20. Medical image registration by combining global and local information: a chain-type diffeomorphic demons algorithm

    International Nuclear Information System (INIS)

    Liu, Xiaozheng; Yuan, Zhenming; Zhu, Junming; Xu, Dongrong

    2013-01-01

    The demons algorithm is a popular algorithm for non-rigid image registration because of its computational efficiency and simple implementation. The deformation forces of the classic demons algorithm were derived from image gradients by considering the deformation to decrease the intensity dissimilarity between images. However, the methods using the difference of image intensity for medical image registration are easily affected by image artifacts, such as image noise, non-uniform imaging and partial volume effects. The gradient magnitude image is constructed from the local information of an image, so the difference in a gradient magnitude image can be regarded as more reliable and robust for these artifacts. Then, registering medical images by considering the differences in both image intensity and gradient magnitude is a straightforward selection. In this paper, based on a diffeomorphic demons algorithm, we propose a chain-type diffeomorphic demons algorithm by combining the differences in both image intensity and gradient magnitude for medical image registration. Previous work had shown that the classic demons algorithm can be considered as an approximation of a second order gradient descent on the sum of the squared intensity differences. By optimizing the new dissimilarity criteria, we also present a set of new demons forces which were derived from the gradients of the image and gradient magnitude image. We show that, in controlled experiments, this advantage is confirmed, and yields a fast convergence. (paper)

  1. The C*-algebra of a vector bundle and fields of Cuntz algebras

    OpenAIRE

    Vasselli, Ezio

    2004-01-01

    We study the Pimsner algebra associated with the module of continuous sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz algebras. We discuss the role of such Pimsner algebras w.r.t. the notion of inner endomorphism. Furthermore, we study bundles of Cuntz algebras carrying a global circle action, and assign to them a class in the representable KK-group of the zero-grade bundle. We compute such class for the Pimsner algebra of a vector bundle.

  2. Bicovariant quantum algebras and quantum Lie algebras

    International Nuclear Information System (INIS)

    Schupp, P.; Watts, P.; Zumino, B.

    1993-01-01

    A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(G q ) to U q g, given by elements of the pure braid group. These operators - the 'reflection matrix' Y= triple bond L + SL - being a special case - generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N). (orig.)

  3. Simple relation algebras

    CERN Document Server

    Givant, Steven

    2017-01-01

    This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatme...

  4. Boolean algebra

    CERN Document Server

    Goodstein, R L

    2007-01-01

    This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.

  5. Combinatorial commutative algebra

    CERN Document Server

    Miller, Ezra

    2005-01-01

    Offers an introduction to combinatorial commutative algebra, focusing on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determined rings. The chapters in this work cover topics ranging from homological invariants of monomial ideals and their polyhedral resolutions, to tools for studying algebraic varieties.

  6. Topological أ-algebras with Cأ-enveloping algebras II

    Indian Academy of Sciences (India)

    necessarily complete) pro-Cأ-topology which coincides with the relative uniform .... problems in Cأ-algebras, Phillips introduced more general weakly Cأ- .... Banach أ-algebra obtained by completing A=Np in the norm jjxpjjp ¼ pًxق where.

  7. C*-algebras by example

    CERN Document Server

    Davidson, Kenneth R

    1996-01-01

    The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of K-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty yea

  8. Non-freely generated W-algebras and construction of N=2 super W-algebras

    International Nuclear Information System (INIS)

    Blumenhagen, R.

    1994-07-01

    Firstly, we investigate the origin of the bosonic W-algebras W(2, 3, 4, 5), W(2, 4, 6) and W(2, 4, 6) found earlier by direct construction. We present a coset construction for all three examples leading to a new type of finitely, non-freely generated quantum W-algebras, which we call unifying W-algebras. Secondly, we develop a manifest covariant formalism to construct N = 2 super W-algebras explicitly on a computer. Applying this algorithm enables us to construct the first four examples of N = 2 super W-algebras with two generators and the N = 2 super W 4 algebra involving three generators. The representation theory of the former ones shows that all examples could be divided into four classes, the largest one containing the N = 2 special type of spectral flow algebras. Besides the W-algebra of the CP(3) Kazama-Suzuki coset model, the latter example with three generators discloses a second solution which could also be explained as a unifying W-algebra for the CP(n) models. (orig.)

  9. Algebraic conformal field theory

    International Nuclear Information System (INIS)

    Fuchs, J.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica

    1991-11-01

    Many conformal field theory features are special versions of structures which are present in arbitrary 2-dimensional quantum field theories. So it makes sense to describe 2-dimensional conformal field theories in context of algebraic theory of superselection sectors. While most of the results of the algebraic theory are rather abstract, conformal field theories offer the possibility to work out many formulae explicitly. In particular, one can construct the full algebra A-bar of global observables and the endomorphisms of A-bar which represent the superselection sectors. Some explicit results are presented for the level 1 so(N) WZW theories; the algebra A-bar is found to be the enveloping algebra of a Lie algebra L-bar which is an extension of the chiral symmetry algebra of the WZW theory. (author). 21 refs., 6 figs

  10. Matrix regularization of 4-manifolds

    OpenAIRE

    Trzetrzelewski, M.

    2012-01-01

    We consider products of two 2-manifolds such as S^2 x S^2, embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)xSU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N^2 x N^2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S...

  11. Boolean algebra essentials

    CERN Document Server

    Solomon, Alan D

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean

  12. q-deformed Poincare algebra

    International Nuclear Information System (INIS)

    Ogievetsky, O.; Schmidke, W.B.; Wess, J.; Muenchen Univ.; Zumino, B.; Lawrence Berkeley Lab., CA

    1992-01-01

    The q-differential calculus for the q-Minkowski space is developed. The algebra of the q-derivatives with the q-Lorentz generators is found giving the q-deformation of the Poincare algebra. The reality structure of the q-Poincare algebra is given. The reality structure of the q-differentials is also found. The real Laplaacian is constructed. Finally the comultiplication, counit and antipode for the q-Poincare algebra are obtained making it a Hopf algebra. (orig.)

  13. Generalizing the bms3 and 2D-conformal algebras by expanding the Virasoro algebra

    Science.gov (United States)

    Caroca, Ricardo; Concha, Patrick; Rodríguez, Evelyn; Salgado-Rebolledo, Patricio

    2018-03-01

    By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms3 algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called Bk, Ck and Dk algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kač-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.

  14. Introduction to quantum algebras

    International Nuclear Information System (INIS)

    Kibler, M.R.

    1992-09-01

    The concept of a quantum algebra is made easy through the investigation of the prototype algebras u qp (2), su q (2) and u qp (1,1). The latter quantum algebras are introduced as deformations of the corresponding Lie algebras; this is achieved in a simple way by means of qp-bosons. The Hopf algebraic structure of u qp (2) is also discussed. The basic ingredients for the representation theory of u qp (2) are given. Finally, in connection with the quantum algebra u qp (2), the qp-analogues of the harmonic oscillator are discussed and of the (spherical and hyperbolical) angular momenta. (author) 50 refs

  15. Continuum analogues of contragredient Lie algebras

    International Nuclear Information System (INIS)

    Saveliev, M.V.; Vershik, A.M.

    1989-03-01

    We present an axiomatic formulation of a new class of infinite-dimensional Lie algebras - the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras ''continuum Lie algebras''. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential Cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered. (author). 9 refs

  16. Lectures on algebraic statistics

    CERN Document Server

    Drton, Mathias; Sullivant, Seth

    2009-01-01

    How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.

  17. Quiver W-algebras

    Science.gov (United States)

    Kimura, Taro; Pestun, Vasily

    2018-06-01

    For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds-Kac-Moody Lie algebras, their quantum affinizations and associated W-algebras.

  18. Abstract algebra

    CERN Document Server

    Garrett, Paul B

    2007-01-01

    Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal

  19. College algebra

    CERN Document Server

    Kolman, Bernard

    1985-01-01

    College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter c

  20. Twisted classical Poincare algebras

    International Nuclear Information System (INIS)

    Lukierski, J.; Ruegg, H.; Tolstoy, V.N.; Nowicki, A.

    1993-11-01

    We consider the twisting of Hopf structure for classical enveloping algebra U(g), where g is the inhomogeneous rotations algebra, with explicite formulae given for D=4 Poincare algebra (g=P 4 ). The comultiplications of twisted U F (P 4 ) are obtained by conjugating primitive classical coproducts by F element of U(c)xU(c), where c denotes any Abelian subalgebra of P 4 , and the universal R-matrices for U F (P 4 ) are triangular. As an example we show that the quantum deformation of Poincare algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincare algebra. The interpretation of twisted Poincare algebra as describing relativistic symmetries with clustered 2-particle states is proposed. (orig.)

  1. Pre-Algebra Essentials For Dummies

    CERN Document Server

    Zegarelli, Mark

    2010-01-01

    Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to scientific notation and simple variable equations. This guide is also a perfect reference for parents who need to review critical pre-algebra

  2. A LAGRANGIAN GAUSS-NEWTON-KRYLOV SOLVER FOR MASS- AND INTENSITY-PRESERVING DIFFEOMORPHIC IMAGE REGISTRATION.

    Science.gov (United States)

    Mang, Andreas; Ruthotto, Lars

    2017-01-01

    We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.

  3. Representations of quantum bicrossproduct algebras

    International Nuclear Information System (INIS)

    Arratia, Oscar; Olmo, Mariano A del

    2002-01-01

    We present a method to construct induced representations of quantum algebras which have a bicrossproduct structure. We apply this procedure to some quantum kinematical algebras in (1+1) dimensions with this kind of structure: null-plane quantum Poincare algebra, non-standard quantum Galilei algebra and quantum κ-Galilei algebra

  4. Algorithms in Algebraic Geometry

    CERN Document Server

    Dickenstein, Alicia; Sommese, Andrew J

    2008-01-01

    In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

  5. Computer algebra and operators

    Science.gov (United States)

    Fateman, Richard; Grossman, Robert

    1989-01-01

    The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

  6. Abstract Algebra to Secondary School Algebra: Building Bridges

    Science.gov (United States)

    Christy, Donna; Sparks, Rebecca

    2015-01-01

    The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

  7. Equivalency of two-dimensional algebras

    International Nuclear Information System (INIS)

    Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S.

    2011-01-01

    Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author)

  8. Axis Problem of Rough 3-Valued Algebras

    Institute of Scientific and Technical Information of China (English)

    Jianhua Dai; Weidong Chen; Yunhe Pan

    2006-01-01

    The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra. In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.

  9. Enveloping σ-C C C-algebra of a smooth Frechet algebra crossed ...

    Indian Academy of Sciences (India)

    Home; Journals; Proceedings – Mathematical Sciences; Volume 116; Issue 2. Enveloping -*-Algebra of a Smooth Frechet Algebra Crossed Product by R R , K -Theory and Differential Structure in *-Algebras. Subhash J Bhatt. Regular Articles Volume 116 Issue 2 May 2006 pp 161-173 ...

  10. Categories and Commutative Algebra

    CERN Document Server

    Salmon, P

    2011-01-01

    L. Badescu: Sur certaines singularites des varietes algebriques.- D.A. Buchsbaum: Homological and commutative algebra.- S. Greco: Anelli Henseliani.- C. Lair: Morphismes et structures algebriques.- B.A. Mitchell: Introduction to category theory and homological algebra.- R. Rivet: Anneaux de series formelles et anneaux henseliens.- P. Salmon: Applicazioni della K-teoria all'algebra commutativa.- M. Tierney: Axiomatic sheaf theory: some constructions and applications.- C.B. Winters: An elementary lecture on algebraic spaces.

  11. Particle-like structure of Lie algebras

    Science.gov (United States)

    Vinogradov, A. M.

    2017-07-01

    If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.

  12. Dynamical entropy of C* algebras and Von Neumann algebras

    International Nuclear Information System (INIS)

    Connes, A.; Narnhofer, H.; Thirring, W.

    1986-01-01

    The definition of the dynamical entropy is extended for automorphism groups of C * algebras. As example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density. (Author)

  13. Gradings on simple Lie algebras

    CERN Document Server

    Elduque, Alberto

    2013-01-01

    Gradings are ubiquitous in the theory of Lie algebras, from the root space decomposition of a complex semisimple Lie algebra relative to a Cartan subalgebra to the beautiful Dempwolff decomposition of E_8 as a direct sum of thirty-one Cartan subalgebras. This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some nonclassical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form. This work can be used as a textbook for graduate students or as a reference for researchers in Lie theory and neighboring areas.

  14. Topological conformal algebra and BRST algebra in non-critical string theories

    International Nuclear Information System (INIS)

    Fujikawa, Kazuo; Suzuki, Hiroshi.

    1991-03-01

    The operator algebra in non-critical string theories is studied by treating the cosmological term as a perturbation. The algebra of covariantly regularized BRST and related currents contains a twisted N = 2 superconformal algebra only at d = -2 in bosonic strings, and a twisted N = 3 superconformal algebra only at d = ±∞ in spinning strings. The bosonic string at d = -2 is examined by replacing the string coordinate by a fermionic matter with c = -2. The resulting bc-βγ system accommodates various forms of BRST cohomology, and the ghost number assignment and BRST cohomology are different in the c = -2 string theory and two-dimensional topological gravity. (author)

  15. Algebraic K-theory

    CERN Document Server

    Srinivas, V

    1996-01-01

    Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in mathematics. The book is based on lectures given at the author's home institution, the Tata Institute in Bombay, and elsewhere. A detailed appendix on topology was provided in the first edition to make the treatment accessible to readers with a limited background in topology. The second edition also includes an appendix on algebraic geometry that contains the required definitions and results needed to understand the core of the book; this makes the book accessible to a wider audience. A central part of the book is a detailed exposition of the ideas of Quillen as contained in his classic papers "Higher Algebraic K-Theory, I, II." A more elementary proof of the theorem of Merkujev--Suslin is given in this edition; this makes the treatment of this topic self-contained. An application ...

  16. Head First Algebra A Learner's Guide to Algebra I

    CERN Document Server

    Pilone, Tracey

    2008-01-01

    Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything from natural numbers and exponents to solving systems of equations and graphing polynomials. Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive i

  17. Novikov algebras with associative bilinear forms

    Energy Technology Data Exchange (ETDEWEB)

    Zhu Fuhai; Chen Zhiqi [School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 (China)

    2007-11-23

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.

  18. Lie algebra in quantum physics by means of computer algebra

    OpenAIRE

    Kikuchi, Ichio; Kikuchi, Akihito

    2017-01-01

    This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct w...

  19. "Aplicação da reação de heck na sintese de compostos heterociclicos"

    OpenAIRE

    Leonardo Silva Santos

    1999-01-01

    Resumo: A reação de Heck intramolecular para as lactamas 4a, 4b, 4g e 4f forneceu exclusivamente produtos de ciclização 6-exo-trig em bons rendimentos e foram acompanhadas da migração da dupla ligação exocíclica fornecendo o biciclo 5 a partir da g-Iactama 4a, uma mistura em proporção molar aproximadamente igual a 6:1 dos biciclos 7 e 8 a partir da d- lactama 4b, uma mistura dos isômeros 18 e 19 a partir da lactama 4f na proporção molar aproximadamente igual a 2:1, e apenas o produto exocícli...

  20. Tensor spaces and exterior algebra

    CERN Document Server

    Yokonuma, Takeo

    1992-01-01

    This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

  1. Profinite algebras and affine boundedness

    OpenAIRE

    Schneider, Friedrich Martin; Zumbrägel, Jens

    2015-01-01

    We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a topological algebra, whereas for topological groups, rings, semigroups, and distributive lattices, profiniteness turns out to be a purely topological property as it is is equivalent to the underlying topological space being a Stone space. Condensing the core...

  2. Double-partition Quantum Cluster Algebras

    DEFF Research Database (Denmark)

    Jakobsen, Hans Plesner; Zhang, Hechun

    2012-01-01

    A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double parti- tions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping...... together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis....

  3. Algebra II workbook for dummies

    CERN Document Server

    Sterling, Mary Jane

    2014-01-01

    To succeed in Algebra II, start practicing now Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success. Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebr

  4. Very true operators on MTL-algebras

    Directory of Open Access Journals (Sweden)

    Wang Jun Tao

    2016-01-01

    Full Text Available The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.

  5. Poisson hierarchy of discrete strings

    International Nuclear Information System (INIS)

    Ioannidou, Theodora; Niemi, Antti J.

    2016-01-01

    The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

  6. Poisson hierarchy of discrete strings

    Energy Technology Data Exchange (ETDEWEB)

    Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)

    2016-01-28

    The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

  7. Matrix regularization of embedded 4-manifolds

    International Nuclear Information System (INIS)

    Trzetrzelewski, Maciej

    2012-01-01

    We consider products of two 2-manifolds such as S 2 ×S 2 , embedded in Euclidean space and show that the corresponding 4-volume preserving diffeomorphism algebra can be approximated by a tensor product SU(N)⊗SU(N) i.e. functions on a manifold are approximated by the Kronecker product of two SU(N) matrices. A regularization of the 4-sphere is also performed by constructing N 2 ×N 2 matrix representations of the 4-algebra (and as a byproduct of the 3-algebra which makes the regularization of S 3 also possible).

  8. Hopf algebras in noncommutative geometry

    International Nuclear Information System (INIS)

    Varilly, Joseph C.

    2001-10-01

    We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)

  9. W-realization of Lie algebras. Application to so(4,2) and Poincare algebras

    International Nuclear Information System (INIS)

    Barbarin, F.; Ragoucy, E.; Sorba, P.

    1996-05-01

    The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a 'canonical' differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated to - the induced representation technique. (author)

  10. Single-Site Palladium(II) Catalyst for Oxidative Heck Reaction: Catalytic Performance and Kinetic Investigations

    Energy Technology Data Exchange (ETDEWEB)

    Duan, Hui; Li, Mengyang; Zhang, Guanghui; Gallagher, James R.; Huang, Zhiliang; Sun, Yu; Luo, Zhong; Chen, Hongzhong; Miller, Jeffrey T.; Zou, Ruqiang; Lei, Aiwen; Zhao, Yanli

    2015-01-01

    ABSTRACT: The development of organometallic single-site catalysts (SSCs) has inspired the designs of new heterogeneous catalysts with high efficiency. Nevertheless, the application of SSCs in certain modern organic reactions, such as C-C bond formation reactions, has still been less investigated. In this study, a single-site Pd(II) catalyst was developed, where 2,2'-bipyridine-grafted periodic mesoporous organosilica (PMO) was employed as the support of a Pd(II) complex. The overall performance of the single-site Pd(II) catalyst in the oxidative Heck reaction was then investigated. The investigation results show that the catalyst displays over 99% selectivity for the product formation with high reaction yield. Kinetic profiles further confirm its high catalytic efficiency, showing that the rate constant is nearly 40 times higher than that for the free Pd(II) salt. X-ray absorption spectroscopy reveals that the catalyst has remarkable lifetime and recyclability.

  11. Higher dimensional uniformisation and W-geometry

    International Nuclear Information System (INIS)

    Govindarajan, S.

    1995-01-01

    We formulate the uniformisation problem underlying the geometry of W n -gravity using the differential equation approach to W-algebras. We construct W n -space (analogous to superspace in supersymmetry) as an (n-1)-dimensional complex manifold using isomonodromic deformations of linear differential equations. The W n -manifold is obtained by the quotient of a Fuchsian subgroup of PSL(n,R) which acts properly discontinuously on a simply connected domain in bfCP n-1 . The requirement that a deformation be isomonodromic furnishes relations which enable one to convert non-linear W-diffeomorphisms to (linear) diffeomorphisms on the W n -manifold. We discuss how the Teichmueller spaces introduced by Hitchin can then be interpreted as the space of complex structures or the space of projective structures with real holonomy on the W n -manifold. The projective structures are characterised by Halphen invariants which are appropriate generalisations of the Schwarzian. This construction will work for all ''generic'' W-algebras. (orig.)

  12. Area-preserving diffeomorphisms in gauge theory on a non-commutative plane. A lattice study

    International Nuclear Information System (INIS)

    Bietenholz, W.; Bigarini, A.; INFN, Sezione di Perugia; Humboldt-Universitaet, Berlin; Torrielli, A.

    2007-06-01

    We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results confirm the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either. (orig.)

  13. Lie algebras and applications

    CERN Document Server

    Iachello, Francesco

    2015-01-01

    This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...

  14. (Fuzzy) Ideals of BN-Algebras

    Science.gov (United States)

    Walendziak, Andrzej

    2015-01-01

    The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050

  15. Non-relativistic Bondi-Metzner-Sachs algebra

    Science.gov (United States)

    Batlle, Carles; Delmastro, Diego; Gomis, Joaquim

    2017-09-01

    We construct two possible candidates for non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. bms4 algebra is infinite-dimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realization of one of these algebras in terms of the Fourier modes of a free Schrödinger field, mimicking the canonical realization of relativistic bms4 algebra using a free Klein-Gordon field.

  16. The Unitality of Quantum B-algebras

    Science.gov (United States)

    Han, Shengwei; Xu, Xiaoting; Qin, Feng

    2018-02-01

    Quantum B-algebras as a generalization of quantales were introduced by Rump and Yang, which cover the majority of implicational algebras and provide a unified semantic for a wide class of substructural logics. Unital quantum B-algebras play an important role in the classification of implicational algebras. The main purpose of this paper is to construct unital quantum B-algebras from non-unital quantum B-algebras.

  17. On Weak-BCC-Algebras

    Science.gov (United States)

    Thomys, Janus; Zhang, Xiaohong

    2013-01-01

    We describe weak-BCC-algebras (also called BZ-algebras) in which the condition (x∗y)∗z = (x∗z)∗y is satisfied only in the case when elements x, y belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras. PMID:24311983

  18. G-identities of non-associative algebras

    International Nuclear Information System (INIS)

    Bakhturin, Yu A; Zaitsev, M V; Sehgal, S K

    1999-01-01

    The main class of algebras considered in this paper is the class of algebras of Lie type. This class includes, in particular, associative algebras, Lie algebras and superalgebras, Leibniz algebras, quantum Lie algebras, and many others. We prove that if a finite group G acts on such an algebra A by automorphisms and anti-automorphisms and A satisfies an essential G-identity, then A satisfies an ordinary identity of degree bounded by a function that depends on the degree of the original identity and the order of G. We show in the case of ordinary Lie algebras that if L is a Lie algebra, a finite group G acts on L by automorphisms and anti-automorphisms, and the order of G is coprime to the characteristic of the field, then the existence of an identity on skew-symmetric elements implies the existence of an identity on the whole of L, with the same kind of dependence between the degrees of the identities. Finally, we generalize Amitsur's theorem on polynomial identities in associative algebras with involution to the case of alternative algebras with involution

  19. W-realization of Lie algebras. Application to so(4,2) and Poincare algebras

    Energy Technology Data Exchange (ETDEWEB)

    Barbarin, F.; Ragoucy, E.; Sorba, P.

    1996-05-01

    The property of some finite W-algebras to appear as the commutant of a particular subalgebra in a simple Lie algebra G is exploited for the obtention of new G-realizations from a `canonical` differential one. The method is applied to the conformal algebra so(4,2) and therefore yields also results for its Poincare subalgebra. Unitary irreducible representations of these algebras are recognized in this approach, which is naturally compared -or associated to - the induced representation technique. (author). 12 refs.

  20. On Dunkl angular momenta algebra

    Energy Technology Data Exchange (ETDEWEB)

    Feigin, Misha [School of Mathematics and Statistics, University of Glasgow,15 University Gardens, Glasgow G12 8QW (United Kingdom); Hakobyan, Tigran [Yerevan State University,1 Alex Manoogian, 0025 Yerevan (Armenia); Tomsk Polytechnic University,Lenin Ave. 30, 634050 Tomsk (Russian Federation)

    2015-11-17

    We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl(N) version of the subalgebra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

  1. Algebraic computing

    International Nuclear Information System (INIS)

    MacCallum, M.A.H.

    1990-01-01

    The implementation of a new computer algebra system is time consuming: designers of general purpose algebra systems usually say it takes about 50 man-years to create a mature and fully functional system. Hence the range of available systems and their capabilities changes little between one general relativity meeting and the next, despite which there have been significant changes in the period since the last report. The introductory remarks aim to give a brief survey of capabilities of the principal available systems and highlight one or two trends. The reference to the most recent full survey of computer algebra in relativity and brief descriptions of the Maple, REDUCE and SHEEP and other applications are given. (author)

  2. Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra

    CERN Document Server

    Cox, David A; O'Shea, Donal

    2015-01-01

    This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem, and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and, with some supplementation perhaps, for beginning graduate level courses in algebraic geom...

  3. Connections between algebra, combinatorics, and geometry

    CERN Document Server

    Sather-Wagstaff, Sean

    2014-01-01

    Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...

  4. Abstract algebra for physicists

    International Nuclear Information System (INIS)

    Zeman, J.

    1975-06-01

    Certain recent models of composite hadrons involve concepts and theorems from abstract algebra which are unfamiliar to most theoretical physicists. The algebraic apparatus needed for an understanding of these models is summarized here. Particular emphasis is given to algebraic structures which are not assumed to be associative. (2 figures) (auth)

  5. Basic notions of algebra

    CERN Document Server

    Shafarevich, Igor Rostislavovich

    2005-01-01

    This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches

  6. Characterizations of locally C*-algebras

    International Nuclear Information System (INIS)

    Mohammad, N.; Somasundaram, S.

    1991-08-01

    We seek the generalization of the Gelfand-Naimark theorems for locally C*-algebras. Precisely, if A is a unital commutative locally C*-algebra, then it is shown that A is *-isomorphic (topologically and algebraically) to C(Δ). Further, if A is any locally C*-algebra, then it is realized as a closed *-subalgebra of some L(H) up to a topological algebraic *-isomorphism. Also, a brief exposition of the Gelfand-Naimark-Segal construction is given and some of its consequences are discussed. (author). 16 refs

  7. Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras

    NARCIS (Netherlands)

    Put, Marius van der

    1999-01-01

    The Galois theory of linear differential equations is presented, including full proofs. The connection with algebraic groups and their Lie algebras is given. As an application the inverse problem of differential Galois theory is discussed. There are many exercises in the text.

  8. Brauer algebras of type B

    NARCIS (Netherlands)

    Cohen, A.M.; Liu, S.

    2011-01-01

    For each n>0, we define an algebra having many properties that one might expect to hold for a Brauer algebra of type Bn. It is defined by means of a presentation by generators and relations. We show that this algebra is a subalgebra of the Brauer algebra of type Dn+1 and point out a cellular

  9. A course in BE-algebras

    CERN Document Server

    Mukkamala, Sambasiva Rao

    2018-01-01

    This book presents a unified course in BE-algebras with a comprehensive introduction, general theoretical basis and several examples. It introduces the general theoretical basis of BE-algebras, adopting a credible style to offer students a conceptual understanding of the subject. BE-algebras are important tools for certain investigations in algebraic logic, because they can be considered as fragments of any propositional logic containing a logical connective implication and the constant "1", which is considered as the logical value “true”.  Primarily aimed at graduate and postgraduate students of mathematics, it also helps researchers and mathematicians to build a strong foundation in applied abstract algebra. Presenting insights into some of the abstract thinking that constitutes modern abstract algebra, it provides a transition from elementary topics to advanced topics in BE-algebras. With abundant examples and exercises arranged after each section, it offers readers a comprehensive, easy-to-follow int...

  10. sl3-web bases, intermediate crystal bases and categorification

    DEFF Research Database (Denmark)

    Tubbenhauer, Daniel

    2014-01-01

    We give an explicit graded cellular basis of the sl3-web algebra K_S. In order to do this, we identify Kuperberg's basis for the sl3-web space W_S with a version of Leclerc-Toffin's intermediate crystal basis and we identify Brundan, Kleshchev and Wang's degree of tableaux with the weight of flows...... on webs and the q-degree of foams. We use this to give a “foamy” version of Hu and Mathas graded cellular basis of the cyclotomic Hecke algebra which turns out to be a graded cellular basis of the sl3-web algebra K_S. We restrict ourselves to the sl3 case here, but our approach should, up...... to the combinatorics of sln-webs, work for all n>1....

  11. On Associative Conformal Algebras of Linear Growth

    OpenAIRE

    Retakh, Alexander

    2000-01-01

    Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We introduce the notions of conformal identity and unital associative conformal algebras and classify finitely generated simple unital associative conformal algebras of linear growth. These are precisely the complete algebras of conformal endomorphisms of finite ...

  12. The Linear Span of Projections in AH Algebras and for Inclusions of C*-Algebras

    Directory of Open Access Journals (Sweden)

    Dinh Trung Hoa

    2013-01-01

    Full Text Available In the first part of this paper, we show that an AH algebra A=lim→(Ai,ϕi has the LP property if and only if every element of the centre of Ai belongs to the closure of the linear span of projections in A. As a consequence, a diagonal AH-algebra has the LP property if it has small eigenvalue variation in the sense of Bratteli and Elliott. The second contribution of this paper is that for an inclusion of unital C*-algebras P⊂A with a finite Watatani index, if a faithful conditional expectation E:A→P has the Rokhlin property in the sense of Kodaka et al., then P has the LP property under the condition thatA has the LP property. As an application, let A be a simple unital C*-algebra with the LP property, α an action of a finite group G onto Aut(A. If α has the Rokhlin property in the sense of Izumi, then the fixed point algebra AG and the crossed product algebra A ⋊α G have the LP property. We also point out that there is a symmetry on the CAR algebra such that its fixed point algebra does not have the LP property.

  13. Non-commutative multiple-valued logic algebras

    CERN Document Server

    Ciungu, Lavinia Corina

    2014-01-01

    This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects.   A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing.   Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

  14. Automorphic Lie algebras with dihedral symmetry

    International Nuclear Information System (INIS)

    Knibbeler, V; Lombardo, S; A Sanders, J

    2014-01-01

    The concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever–Novikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is sl 2 (C) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits. (paper)

  15. Certain number-theoretic episodes in algebra

    CERN Document Server

    Sivaramakrishnan, R

    2006-01-01

    Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available. Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.

  16. A Note On Signs Of Fourier Coefficients Of Two Cusp Forms

    Indian Academy of Sciences (India)

    10

    Abstract. Kohnen and Sengupta showed that if two Hecke eigen cusp forms of weight k1 and k2 respectively with 1 < k1 < k2 over. Γ0(N ), have totally real algebraic Fourier coefficients {a(n)} and. {b(n)} respectively for n ≥ 1 with a(1) = 1 = b(1), then there exists an element σ of the absolute Galois group Gal(Q/Q) such.

  17. Fusion rules of chiral algebras

    International Nuclear Information System (INIS)

    Gaberdiel, M.

    1994-01-01

    Recently we showed that for the case of the WZW and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral algebras. We define the tensor product of conformal field theory in the general case and prove that it is associative and symmetric up to equivalence. We also determine explicitly the action of the chiral algebra on this tensor product. In the second part of the paper we demonstrate that this framework provides a powerful tool for calculating restrictions for the fusion rules of chiral algebras. We exhibit this for the case of the W 3 algebra and the N=1 and N=2 NS superconformal algebras. (orig.)

  18. Computations in finite-dimensional Lie algebras

    Directory of Open Access Journals (Sweden)

    A. M. Cohen

    1997-12-01

    Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.

  19. Coset realization of unifying W-algebras

    International Nuclear Information System (INIS)

    Blumenhagen, R.; Huebel, R.

    1994-06-01

    We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and sl(2,R)+sl(2,R)/sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W-algebras of Casimir W-algebras. We show that it is possible to give coset realizations of various types of unifying W-algebras, e.g. the diagonal cosets based on the symplectic Lie algebras sp(2n) realize the unifying W-algebras which have previously been introduced as 'WD -n '. In addition, minimal models of WD -n are studied. The coset realizations provide a generalization of level-rank-duality of dual coset pairs. As further examples of finitely nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras which on the quantum level has different properties than in the classical case. We demonstrate in some examples that the classical limit according to Bowcock and Watts of these nonfreely finitely generated quantum W-algebras probably yields infinitely nonfreely generated classical W-algebras. (orig.)

  20. Combined experimental and theoretical study of the mechanism and enantioselectivity of palladium-catalyzed intermolecular Heck coupling

    DEFF Research Database (Denmark)

    Henriksen, Signe Teuber; Norrby, Per-Ola; Kaukoranta, Päivi

    2008-01-01

    . The steric interactions in this transition state fully account for the enantioselectivity observed with the ligands studied. The calculations also predict relative reactivity and nonlinear mixing effects for the investigated ligands; these predictions are fully validated by experimental testing. Finally......The asymmetric Heck reaction using P,N-ligands has been studied by a combination of theoretical and experimental methods. The reaction follows Halpern-style selectivity; that is, the major isomer is produced from the least favored form of the pre-insertion intermediate. The initially formed Ph......, the low conversion observed with some catalysts was found to be caused by inactivation due to weak binding of the ligand to Pd(0). Adding monodentate PPh3 alleviated the precipitation problem without deteriorating the enantioselectivity and led to one of the most effective catalytic systems to date....

  1. Algebra

    CERN Document Server

    Sepanski, Mark R

    2010-01-01

    Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems

  2. Identities and derivations for Jacobian algebras

    International Nuclear Information System (INIS)

    Dzhumadil'daev, A.S.

    2001-09-01

    Constructions of n-Lie algebras by strong n-Lie-Poisson algebras are given. First cohomology groups of adjoint module of Jacobian algebras are calculated. Minimal identities of 3-Jacobian algebra are found. (author)

  3. Situating the Debate on "Geometrical Algebra" within the Framework of Premodern Algebra.

    Science.gov (United States)

    Sialaros, Michalis; Christianidis, Jean

    2016-06-01

    Argument The aim of this paper is to employ the newly contextualized historiographical category of "premodern algebra" in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on "geometrical algebra." Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called "semi-algebraic" alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing "premodern algebra," and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

  4. Cohomology of Effect Algebras

    Directory of Open Access Journals (Sweden)

    Frank Roumen

    2017-01-01

    Full Text Available We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Kunneth and Mayer-Vietoris sequences. The second way involves a chain complex of ordered abelian groups, and gives rise to a cohomological characterization of state extensions on effect algebras. This has applications to no-go theorems in quantum foundations, such as Bell's theorem.

  5. Algebra and Arithmetic of Modular Forms

    DEFF Research Database (Denmark)

    Rustom, Nadim

    In [Rus14b] and [Rus14a], we study graded rings of modular forms over congruence subgroups, with coefficients in subrings A of C, and determine bounds of the weights of modular forms constituting a minimal set of generators, as well as on the degree of the generators of the ideal of relations...... between them. We give an algorithm that computes the structures of these rings, and formulate conjectures on the minimal generating weight for modular forms with coefficients in Z. We discuss questions of finiteness of systems of Hecke eigenvalues modulo pm, for a prime p and an integer m ≥ 2, in analogy...

  6. Case Report of Focal Epithelial Hyperplasia (Heck's Disease) with Polymerase Chain Reaction Detection of Human Papillomavirus 13.

    Science.gov (United States)

    Brehm, Mary A; Gordon, Katie; Firan, Miahil; Rady, Peter; Agim, Nnenna

    2016-05-01

    Focal epithelial hyperplasia (FEH), or Heck's disease, is an uncommon benign proliferation of oral mucosa caused by the human papillomavirus (HPV), particularly subtypes 13 and 32. The disease typically presents in young Native American patients and is characterized by multiple asymptomatic papules and nodules on the oral mucosa, lips, tongue, and gingiva. The factors that determine susceptibility to FEH are unknown, but the ethnic and geographic distribution of FEH suggests that genetic predisposition, particularly having the human lymphocytic antigen DR4 type, may be involved in pathogenesis. We report a case of FEH with polymerase chain reaction detection of HPV13 in a healthy 11-year-old Hispanic girl and discuss the current understanding of disease pathogenesis, susceptibility, and treatment. © 2016 Wiley Periodicals, Inc.

  7. Investigating the nature of palladium chain-walking in the enantioselective redox-relay Heck reaction of alkenyl alcohols.

    Science.gov (United States)

    Hilton, Margaret J; Xu, Li-Ping; Norrby, Per-Ola; Wu, Yun-Dong; Wiest, Olaf; Sigman, Matthew S

    2014-12-19

    The mechanism of the redox-relay Heck reaction was investigated using deuterium-labeled substrates. Results support a pathway through a low energy palladium-alkyl intermediate that immediately precedes product formation, ruling out a tautomerization mechanism. DFT calculations of the relevant transition structures at the M06/LAN2DZ+f/6-31+G* level of theory show that the former pathway is favored by 5.8 kcal/mol. Palladium chain-walking toward the alcohol, following successive β-hydride eliminations and migratory insertions, is also supported in this study. The stereochemistry of deuterium labels is determined, lending support that the catalyst remains bound to the substrate during the relay process and that both cis- and trans-alkenes form from β-hydride elimination.

  8. Topology general & algebraic

    CERN Document Server

    Chatterjee, D

    2007-01-01

    About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the

  9. Graded associative conformal algebras of finite type

    OpenAIRE

    Kolesnikov, Pavel

    2011-01-01

    In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\\Gamma $ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\\simeq \\Gamma $. A classification of simple...

  10. Principles of linear algebra with Mathematica

    CERN Document Server

    Shiskowski, Kenneth M

    2013-01-01

    A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for visualizing many of the geometric aspects within this field of study. Principles of Linear Algebra with Mathematica uniquely bridges the gap between beginning linear algebra and computational linear algebra that is often encountered in applied settings,

  11. Einstein algebras and general relativity

    International Nuclear Information System (INIS)

    Heller, M.

    1992-01-01

    A purely algebraic structure called an Einstein algebra is defined in such a way that every spacetime satisfying Einstein's equations is an Einstein algebra but not vice versa. The Gelfand representation of Einstein algebras is defined, and two of its subrepresentations are discussed. One of them is equivalent to the global formulation of the standard theory of general relativity; the other one leads to a more general theory of gravitation which, in particular, includes so-called regular singularities. In order to include other types of singularities one must change to sheaves of Einstein algebras. They are defined and briefly discussed. As a test of the proposed method, the sheaf of Einstein algebras corresponding to the space-time of a straight cosmic string with quasiregular singularity is constructed. 22 refs

  12. Analytic real algebras.

    Science.gov (United States)

    Seo, Young Joo; Kim, Young Hee

    2016-01-01

    In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for real-valued functions to be a (edge) d -algebra.

  13. Biderivations of W-algebra $W(2,2)$ and Virasoro algebra without skewsymmetric condition and their applications

    OpenAIRE

    Tang, Xiaomin

    2016-01-01

    In this paper, we characterize the biderivations of W-algebra $W(2,2)$ and Virasoro algebra $Vir$ without skewsymmetric condition. We get two classes of non-inner biderivations. As applications, we also get the forms of linear commuting maps on W-algebra $W(2,2)$ and Virasoro algebra $Vir$.

  14. Evolution algebras generated by Gibbs measures

    International Nuclear Information System (INIS)

    Rozikov, Utkir A.; Tian, Jianjun Paul

    2009-03-01

    In this article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the function spaces (cell spaces) defined by graphs and state spaces and Gibbs measure μ. For finite graphs we find some evolution subalgebras and other useful properties of the algebras. We obtain a structure theorem for evolution algebras when graphs are finite and connected. We prove that for a fixed finite graph, the function spaces have a unique algebraic structure since all evolution algebras are isomorphic to each other for whichever Gibbs measures are assigned. When graphs are infinite graphs then our construction allows a natural introduction of thermodynamics in studying of several systems of biology, physics and mathematics by theory of evolution algebras. (author)

  15. Classical algebraic chromodynamics

    International Nuclear Information System (INIS)

    Adler, S.L.

    1978-01-01

    I develop an extension of the usual equations of SU(n) chromodynamics which permits the consistent introduction of classical, noncommuting quark source charges. The extension involves adding a singlet gluon, giving a U(n) -based theory with outer product P/sup a/(u,v) = (1/2)(d/sup a/bc + if/sup a/bc)(u/sup b/v/sup c/ - v/sup b/u/sup c/) which obeys the Jacobi identity, inner product S (u,v) = (1/2)(u/sup a/v/sup a/ + v/sup a/u/sup a/), and with the n 2 gluon fields elevated to algebraic fields over the quark color charge C* algebra. I show that provided the color charge algebra satisfies the condition S (P (u,v),w) = S (u,P (v,w)) for all elements u,v,w of the algebra, all the standard derivations of Lagrangian chromodynamics continue to hold in the algebraic chromodynamics case. I analyze in detail the color charge algebra in the two-particle (qq, qq-bar, q-barq-bar) case and show that the above consistency condition is satisfied for the following unique (and, interestingly, asymmetric) choice of quark and antiquark charges: Q/sup a//sub q/ = xi/sup a/, Q/sup a//sub q/ = xi-bar/sup a/ + delta/sup a/0(n/2)/sup 3/2/1, with xi/sup a/xi/sup b/ = (1/2)(d/sup a/bc + if/sup a/bc) xi/sup c/, xi-bar/sup a/xi-bar/sup b/ = -(1/2)(d/sup a/bc - if/sup a/bc) xi-bar/sup c/. The algebraic structure of the two-particle U(n) force problem, when expressed on an appropriately diagonalized basis, leads for all n to a classical dynamics problem involving an ordinary SU(2) Yang-Mills field with uniquely specified classical source charges which are nonparallel in the color-singlet state. An explicit calculation shows that local algebraic U(n) gauge transformations lead only to a rigid global rotation of axes in the overlying classical SU(2) problem, which implies that the relative orientations of the classical source charges have physical significance

  16. On the classification of quantum W-algebras

    International Nuclear Information System (INIS)

    Bowcock, P.; Watts, G.T.M.

    1992-01-01

    In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each reductive W-algebra. The finite Lie algebra is also endowed with a preferred sl(2) subalgebra, which gives the conformal weights of the W-algebra. We extend this to cover W-algebras containing both bosonic and fermionic fields, and illustrate our ideas with the Poisson bracket algebras of generalised Drinfeld-Sokolov hamiltonian systems. We then discuss the possibilities of classifying deformable W-algebras which fall outside this class in the context of automorphisms of Lie algebras. In conclusion we list the cases in which the W-algebra has no weight-one fields, and further, those in which it has only one weight-two field. (orig.)

  17. Shape-based diffeomorphic registration on hippocampal surfaces using Beltrami holomorphic flow.

    Science.gov (United States)

    Lui, Lok Ming; Wong, Tsz Wai; Thompson, Paul; Chan, Tony; Gu, Xianfeng; Yau, Shing-Tung

    2010-01-01

    We develop a new algorithm to automatically register hippocampal (HP) surfaces with complete geometric matching, avoiding the need to manually label landmark features. A good registration depends on a reasonable choice of shape energy that measures the dissimilarity between surfaces. In our work, we first propose a complete shape index using the Beltrami coefficient and curvatures, which measures subtle local differences. The proposed shape energy is zero if and only if two shapes are identical up to a rigid motion. We then seek the best surface registration by minimizing the shape energy. We propose a simple representation of surface diffeomorphisms using Beltrami coefficients, which simplifies the optimization process. We then iteratively minimize the shape energy using the proposed Beltrami Holomorphic flow (BHF) method. Experimental results on 212 HP of normal and diseased (Alzheimer's disease) subjects show our proposed algorithm is effective in registering HP surfaces with complete geometric matching. The proposed shape energy can also capture local shape differences between HP for disease analysis.

  18. Lie-Algebras. Pt. 1

    International Nuclear Information System (INIS)

    Baeuerle, G.G.A.; Kerf, E.A. de

    1990-01-01

    The structure of the laws in physics is largely based on symmetries. This book is on Lie algebras, the mathematics of symmetry. It gives a thorough mathematical treatment of finite dimensional Lie algebras and Kac-Moody algebras. Concepts such as Cartan matrix, root system, Serre's construction are carefully introduced. Although the book can be read by an undergraduate with only an elementary knowledge of linear algebra, the book will also be of use to the experienced researcher. Experience has shown that students who followed the lectures are well-prepared to take on research in the realms of string-theory, conformal field-theory and integrable systems. 48 refs.; 66 figs.; 3 tabs

  19. Semiprojectivity of universal -algebras generated by algebraic elements

    DEFF Research Database (Denmark)

    Shulman, Tatiana

    2012-01-01

    Let be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal -algebra of a relation , , is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given.......Let be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal -algebra of a relation , , is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given....

  20. The formal theory of Hopf algebras part II: the case of Hopf algebras ...

    African Journals Online (AJOL)

    The category HopfR of Hopf algebras over a commutative unital ring R is analyzed with respect to its categorical properties. The main results are: (1) For every ring R the category HopfR is locally presentable, it is coreflective in the category of bialgebras over R, over every R-algebra there exists a cofree Hopf algebra. (2) If ...

  1. Macdonald index and chiral algebra

    Science.gov (United States)

    Song, Jaewon

    2017-08-01

    For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type ( A 1 , A 2 n ) and ( A 1 , D 2 n+1) where the chiral algebras are given by Virasoro and \\widehat{su}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.

  2. Vertex algebras and mirror symmetry

    International Nuclear Information System (INIS)

    Borisov, L.A.

    2001-01-01

    Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish the relation between these vertex algebras for mirror Calabi-Yau manifolds. This should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras. Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras. Ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties.This paper could also be of interest to physicists, because it contains explicit description of holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in terms of free bosons and fermions. (orig.)

  3. Advanced modern algebra part 2

    CERN Document Server

    Rotman, Joseph J

    2017-01-01

    This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

  4. A q-deformed Lorentz algebra

    International Nuclear Information System (INIS)

    Schmidke, W.B.; Wess, J.; Muenchen Univ.; Zumino, B.; Lawrence Berkeley Lab., CA

    1991-01-01

    We derive a q-deformed version of the Lorentz algebra by deformating the algebra SL(2, C). The method is based on linear representations of the algebra on the complex quantum spinor space. We find that the generators usually identified with SL q (2, C) generate SU q (2) only. Four additional generators are added which generate Lorentz boosts. The full algebra of all seven generators and their coproduct is presented. We show that in the limit q→1 the generators are those of the classical Lorentz algebra plus an additional U(1). Thus we have a deformation of SL(2, C)xU(1). (orig.)

  5. Introduction to algebraic quantum field theory

    International Nuclear Information System (INIS)

    Horuzhy, S.S.

    1990-01-01

    This volume presents a systematic introduction to the algebraic approach to quantum field theory. The structure of the contents corresponds to the way the subject has advanced. It is shown how the algebraic approach has developed from the purely axiomatic theory of observables via superselection rules into the dynamical formalism of fields and observables. Chapter one discusses axioms and their consequences -many of which are now classical theorems- and deals, in general, with the axiomatic theory of local observable algebras. The absence of field concepts makes this theory incomplete and, in chapter two, superselection rules are shown to be the key to the reconstruction of fields from observables. Chapter three deals with the algebras of Wightman fields, first unbounded operator algebras, then Von Neumann field algebras (with a special section on wedge region algebras) and finally local algebras of free and generalised free fields. (author). 447 refs.; 4 figs

  6. Comments on N=4 superconformal algebras

    International Nuclear Information System (INIS)

    Rasmussen, J.

    2001-01-01

    We present a new and asymmetric N=4 superconformal algebra for arbitrary central charge, thus completing our recent work on its classical analogue with vanishing central charge. Besides the Virasoro generator and 4 supercurrents, the algebra consists of an internal SU(2)xU(1) Kac-Moody algebra in addition to two spin 1/2 fermions and a bosonic scalar. The algebra is shown to be invariant under a linear twist of the generators, except for a unique value of the continuous twist parameter. At this value, the invariance is broken and the algebra collapses to the small N=4 superconformal algebra. The asymmetric N=4 superconformal algebra may be seen as induced by an affine SL(2 vertical bar 2) current superalgebra. Replacing SL(2 vertical bar 2) with the coset SL(2 vertical bar 2)/U(1), results directly in the small N=4 superconformal algebra

  7. The theory of algebraic numbers

    CERN Document Server

    Pollard, Harry

    1998-01-01

    An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.

  8. Quantum Heisenberg groups and Sklyanin algebras

    International Nuclear Information System (INIS)

    Andruskiewitsch, N.; Devoto, J.; Tiraboschi, A.

    1993-05-01

    We define new quantizations of the Heisenberg group by introducing new quantizations in the universal enveloping algebra of its Lie algebra. Matrix coefficients of the Stone-von Neumann representation are preserved by these new multiplications on the algebra of functions on the Heisenberg group. Some of the new quantizations provide also a new multiplication in the algebra of theta functions; we obtain in this way Sklyanin algebras. (author). 23 refs

  9. Classification of simple flexible Lie-admissible algebras

    International Nuclear Information System (INIS)

    Okubo, S.; Myung, H.C.

    1979-01-01

    Let A be a finite-dimensional flexible Lie-admissible algebra over the complex field such that A - is a simple Lie algebra. It is shown that either A is itself a Lie algebra isomorphic to A - or A - is a Lie algebra of type A/sub n/ (n greater than or equal to 2). In the latter case, A is isomorphic to the algebra defined on the space of (n + 1) x (n + 1) traceless matrices with multiplication given by x * y = μxy + (1 - μ)yx - (1/(n + 100 Tr (xy) E where μ is a fixed scalar, xy denotes the matrix operators in Lie algebras which has been studied in theoretical physics. We also discuss a broader class of Lie algebras over arbitrary field of characteristic not equal to 2, called quasi-classical, which includes semisimple as well as reductive Lie algebras. For this class of Lie algebras, we can introduce a multiplication which makes the adjoint operator space into an associative algebra. When L is a Lie algebra with nondegenerate killing form, it is shown that the adjoint operator algebra of L in the adjoint representation becomes a commutative associative algebra with unit element and its dimension is 1 or 2 if L is simple over the complex field. This is related to the known result that a Lie algebra of type A/sub n/ (n greater than or equal to 2) alone has a nonzero completely symmetric adjoint operator in the adjoint representation while all other algebras have none. Finally, Lie-admissible algebras associated with bilinear form are investigated

  10. Pd-isatin Schiff base complex immobilized onγ-Fe2O3 as a magnetically recyclable catalyst for the Heck and Suzuki cross-coupling reactions

    Institute of Scientific and Technical Information of China (English)

    Sara Sobhani; Farzaneh Zarifi

    2015-01-01

    A Pd‐isatin Schiff base complex immobilized onγ‐Fe2O3 (Pd‐isatin Schiff base‐γ‐Fe2O3) was synthe‐sized and characterized by Fourier transform infrared, scanning electron microscopy, high resolu‐tion transmission electron microscopy, X‐ray diffraction, thermogravimetric gravimetric analysis, inductively‐coupled plasma, X‐ray photoelectron spectroscopy, and elemental analysis. It was used as a magnetically reusable Pd catalyst for the Heck and Suzuki cross‐coupling reactions.

  11. Quantitative Algebraic Reasoning

    DEFF Research Database (Denmark)

    Mardare, Radu Iulian; Panangaden, Prakash; Plotkin, Gordon

    2016-01-01

    We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We define an equality relation indexed by rationals: a =ε b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative...... equational theory whose free algebras correspond to well known structures. In each case we have finitary and continuous versions. The four cases are: Hausdorff metrics from quantitive semilattices; pWasserstein metrics (hence also the Kantorovich metric) from barycentric algebras and also from pointed...

  12. Anyons, deformed oscillator algebras and projectors

    International Nuclear Information System (INIS)

    Engquist, Johan

    2009-01-01

    We initiate an algebraic approach to the many-anyon problem based on deformed oscillator algebras. The formalism utilizes a generalization of the deformed Heisenberg algebras underlying the operator solution of the Calogero problem. We define a many-body Hamiltonian and an angular momentum operator which are relevant for a linearized analysis in the statistical parameter ν. There exists a unique ground state and, in spite of the presence of defect lines, the anyonic weight lattices are completely connected by the application of the oscillators of the algebra. This is achieved by supplementing the oscillator algebra with a certain projector algebra.

  13. Alternative algebraic approaches in quantum chemistry

    International Nuclear Information System (INIS)

    Mezey, Paul G.

    2015-01-01

    Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed

  14. Alternative algebraic approaches in quantum chemistry

    Energy Technology Data Exchange (ETDEWEB)

    Mezey, Paul G., E-mail: paul.mezey@gmail.com [Canada Research Chair in Scientific Modeling and Simulation, Department of Chemistry and Department of Physics and Physical Oceanography, Memorial University of Newfoundland, 283 Prince Philip Drive, St. John' s, NL A1B 3X7 (Canada)

    2015-01-22

    Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.

  15. On graded algebras of global dimension 3

    International Nuclear Information System (INIS)

    Piontkovskii, D I

    2001-01-01

    Assume that a graded associative algebra A over a field k is minimally presented as the quotient algebra of a free algebra F by the ideal I generated by a set f of homogeneous elements. We study the following two extensions of A: the algebra F-bar=F/I oplus I/I 2 oplus ... associated with F with respect to the I-adic filtration, and the homology algebra H of the Shafarevich complex Sh(f,F) (which is a non-commutative version of the Koszul complex). We obtain several characterizations of algebras of global dimension 3. In particular, the A-algebra H in this case is free, and the algebra F-bar is isomorphic to the quotient algebra of a free A-algebra by the ideal generated by a so-called strongly free (or inert) set

  16. Unipotent and nilpotent classes in simple algebraic groups and lie algebras

    CERN Document Server

    Liebeck, Martin W

    2012-01-01

    This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of...

  17. Elements of mathematics algebra

    CERN Document Server

    Bourbaki, Nicolas

    2003-01-01

    This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, Algèbre, Chapters 4 to 7 (1981). This completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 was entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and...

  18. Brauer algebra of type F4

    NARCIS (Netherlands)

    Liu, S.

    2012-01-01

    We present an algebra related to the Coxeter group of type F4 which can be viewed as the Brauer algebra of type F4 and is obtained as a subalgebra of the Brauer algebra of type E6. We also describe some properties of this algebra.

  19. Brauer algebras of type F4

    NARCIS (Netherlands)

    Liu, S.

    2013-01-01

    We present an algebra related to the Coxeter group of type F4 which can be viewed as the Brauer algebra of type F4 and is obtained as a subalgebra of the Brauer algebra of type E6. We also describe some properties of this algebra.

  20. QFT holography near the horizon of Schwarzschild-like spacetimes

    OpenAIRE

    Moretti, Valter; Pinamonti, Nicola

    2003-01-01

    It is argued that free QFT can be defined on the event horizon of a Schwarzschild-like spacetime and that this theory is unitarily and algebraically equivalent to QFT in the bulk (near the horizon). Under that unitary equivalence the bulk hidden SL(2,R) symmetry found in a previous work becomes manifest on the event horizon, it being induced by a group of horizon diffeomorphisms. The class of generators of that group can be enlarged to include a full Virasoro algebra of fields which are defin...

  1. Generalized Galilean algebras and Newtonian gravity

    Science.gov (United States)

    González, N.; Rubio, G.; Salgado, P.; Salgado, S.

    2016-04-01

    The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

  2. Circle Maps and C*-algebras

    DEFF Research Database (Denmark)

    Schmidt, Thomas Lundsgaard

    such a map, generalising the transformation groupoid of a local homeomorphism first introduced by Renault in \\cite{re}. We conduct a detailed study of the relationship between the dynamics of $\\phi$, the properties of these groupoids, the structure of their corresponding reduced groupoid $C^*$-algebras, and......, for certain classes of maps, the K-theory of these algebras. When the map $\\phi$ is transitive, we show that the algebras $C^*_r(\\Gamma_\\phi)$ and $C^*_r(\\Gamma_\\phi^+)$ are purely infinite and satisfy the Universal Coefficient Theorem. Furthermore, we find necessary and sufficient conditions for simplicity...... of these algebras in terms of dynamical properties of $\\phi$. We proceed to consider the situation when the algebras are non-simple, and describe the primitive ideal spectrum in this case. We prove that any irreducible representation factors through the $C^*$-algebra of the reduction of the groupoid to the orbit...

  3. The Boolean algebra of Galois algebras

    Directory of Open Access Journals (Sweden)

    Lianyong Xue

    2003-02-01

    Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(xb for all x∈B} for each g∈G, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero element in Ba, and He={g∈G|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generated by e with Galois group He, is investigated.

  4. Geometry of Spin: Clifford Algebraic Approach

    Indian Academy of Sciences (India)

    Then the various algebraic properties of Pauli matricesare studied as properties of matrix algebra. What has beenshown in this article is that Pauli matrices are a representationof Clifford algebra of spin and hence all the propertiesof Pauli matrices follow from the underlying algebra. Cliffordalgebraic approach provides a ...

  5. Differential operators and W-algebra

    International Nuclear Information System (INIS)

    Vaysburd, I.; Radul, A.

    1992-01-01

    The connection between W-algebras and the algebra of differential operators is conjectured. The bosonized representation of the differential operator algebra with c=-2n and all the subalgebras are examined. The degenerate representations and null-state classifications for c=-2 are presented. (orig.)

  6. Donaldson invariants in algebraic geometry

    International Nuclear Information System (INIS)

    Goettsche, L.

    2000-01-01

    In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

  7. Fractional supersymmetry and infinite dimensional lie algebras

    International Nuclear Information System (INIS)

    Rausch de Traubenberg, M.

    2001-01-01

    In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation D of any Lie algebra g. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of g this infinite dimensional Lie algebra, containing the Lie algebra g as a sub-algebra, is explicitly constructed

  8. Quantum algebra of N superspace

    International Nuclear Information System (INIS)

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-01-01

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the κ-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra

  9. Tetradentate N2O2 Chelated Palladium(II Complexes: Synthesis, Characterization, and Catalytic Activity towards Mizoroki-Heck Reaction of Aryl Bromides

    Directory of Open Access Journals (Sweden)

    Siti Kamilah Che Soh

    2013-01-01

    Full Text Available Four air and moisture-stable palladium(II-Schiff base complexes, N,N′-bis(α-methylsalicylidenepropane-1,3-diamine palladium(II (2a, N,N′-bis(4-methyl-α-methylsalicylidenepropane-1,3-diamine palladium(II (2b, N,N′-bis(3,5-di-tert-butylsalicylidenepropane-1,3-diamine palladium(II (2c, and N,N′-bis(4-methoxy-salicylidenepropane-1,3-diamine palladium(II (2d, have been successfully synthesised and characterised by CHN elemental analyses and conventional spectroscopic methods. These complexes were investigated as catalysts in the phosphine-free Mizoroki-Heck cross-coupling reactions of aryl bromides with methyl acrylate.

  10. On criteria for algebraic independence of collections of functions satisfying algebraic difference relations

    Directory of Open Access Journals (Sweden)

    Hiroshi Ogawara

    2017-01-01

    Full Text Available This paper gives conditions for algebraic independence of a collection of functions satisfying a certain kind of algebraic difference relations. As applications, we show algebraic independence of two collections of special functions: (1 Vignéras' multiple gamma functions and derivatives of the gamma function, (2 the logarithmic function, \\(q\\-exponential functions and \\(q\\-polylogarithm functions. In a similar way, we give a generalization of Ostrowski's theorem.

  11. An algebra of reversible computation.

    Science.gov (United States)

    Wang, Yong

    2016-01-01

    We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.

  12. On an extension of the Weil algebra

    International Nuclear Information System (INIS)

    Palev, Ch.

    An extension of the Weil algebra Wsub(n), generated by an appropriate topology is considered. The topology is introduced in such a way that algebraic operations in Wsub(n) to be continuous. The algebraic operations in Wsub(n) are extended by a natural way to a complement, which is noted as an extended Weil algebra. It turns out that the last algebra contains isomorphically the Heisenberg group. By the same way an arbitrary enveloping algebra of a Lie group may be extended. The extended algebra will contain the initial Lie group. (S.P.)

  13. Raising and Lowering Operators for Askey-Wilson Polynomials

    Directory of Open Access Journals (Sweden)

    Siddhartha Sahi

    2007-01-01

    Full Text Available In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the ''classical'' properties of these polynomials, viz. the q-difference equation and the three term recurrence. The second technique is less elementary, and involves the one-variable version of the double affine Hecke algebra.

  14. Exponentiation and deformations of Lie-admissible algebras

    International Nuclear Information System (INIS)

    Myung, H.C.

    1982-01-01

    The exponential function is defined for a finite-dimensional real power-associative algebra with unit element. The application of the exponential function is focused on the power-associative (p,q)-mutation of a real or complex associative algebra. Explicit formulas are computed for the (p,q)-mutation of the real envelope of the spin 1 algebra and the Lie algebra so(3) of the rotation group, in light of earlier investigations of the spin 1/2. A slight variant of the mutated exponential is interpreted as a continuous function of the Lie algebra into some isotope of the corresponding linear Lie group. The second part of this paper is concerned with the representation and deformation of a Lie-admissible algebra. The second cohomology group of a Lie-admissible algebra is introduced as a generalization of those of associative and Lie algebras in the Hochschild and Chevalley-Eilenberg theory. Some elementary theory of algebraic deformation of Lie-admissible algebras is discussed in view of generalization of that of associative and Lie algebras. Lie-admissible deformations are also suggested by the representation of Lie-admissible algebras. Some explicit examples of Lie-admissible deformation are given in terms of the (p,q)-mutation of associative deformation of an associative algebra. Finally, we discuss Lie-admissible deformations of order one

  15. Clifford algebras and the minimal representations of the 1D N-extended supersymmetry algebra

    International Nuclear Information System (INIS)

    Toppan, Francesco

    2008-01-01

    The Atiyah-Bott-Shapiro classification of the irreducible Clifford algebra is used to derive general properties of the minimal representations of the 1D N-Extended Supersymmetry algebra (the Z 2 -graded symmetry algebra of the Supersymmetric Quantum Mechanics) linearly realized on a finite number of fields depending on a real parameter t, the time. (author)

  16. Contraction of graded su(2) algebra

    International Nuclear Information System (INIS)

    Patra, M.K.; Tripathy, K.C.

    1989-01-01

    The Inoenu-Wigner contraction scheme is extended to Lie superalgebras. The structure and representations of extended BRS algebra are obtained from contraction of the graded su(2) algebra. From cohomological consideration, we demonstrate that the graded su(2) algebra is the only superalgebra which, on contraction, yields the full BRS algebra. (orig.)

  17. Atomic effect algebras with compression bases

    International Nuclear Information System (INIS)

    Caragheorgheopol, Dan; Tkadlec, Josef

    2011-01-01

    Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

  18. Operator theory, operator algebras and applications

    CERN Document Server

    Lebre, Amarino; Samko, Stefan; Spitkovsky, Ilya

    2014-01-01

    This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geo...

  19. A twisted generalization of Novikov-Poisson algebras

    OpenAIRE

    Yau, Donald

    2010-01-01

    Hom-Novikov-Poisson algebras, which are twisted generalizations of Novikov-Poisson algebras, are studied. Hom-Novikov-Poisson algebras are shown to be closed under tensor products and several kinds of twistings. Necessary and sufficient conditions are given under which Hom-Novikov-Poisson algebras give rise to Hom-Poisson algebras.

  20. Process Algebra and Markov Chains

    NARCIS (Netherlands)

    Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.

    This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

  1. Process algebra and Markov chains

    NARCIS (Netherlands)

    Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.

    2001-01-01

    This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

  2. Vertex ring-indexed Lie algebras

    International Nuclear Information System (INIS)

    Fairlie, David; Zachos, Cosmas

    2005-01-01

    Infinite-dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalizations of the Onsager algebra, but unlike it, or its sl(n) generalizations, they are not subalgebras of the loop algebras associated with sl(n). In a particular interesting case associated with sl(3), their indices lie on the Eisenstein integer triangular lattice, and these algebras are expected to underlie vertex operator combinations in CFT, brane physics, and graphite monolayers

  3. Invariants of triangular Lie algebras

    International Nuclear Information System (INIS)

    Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

    2007-01-01

    Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated

  4. Q-systems as cluster algebras

    International Nuclear Information System (INIS)

    Kedem, Rinat

    2008-01-01

    Q-systems first appeared in the analysis of the Bethe equations for the XXX model and generalized Heisenberg spin chains (Kirillov and Reshetikhin 1987 Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Steklov. 160 211-21, 301). Such systems are known to exist for any simple Lie algebra and many other Kac-Moody algebras. We formulate the Q-system associated with any simple, simply-laced Lie algebras g in the language of cluster algebras (Fomin and Zelevinsky 2002 J. Am. Math. Soc. 15 497-529), and discuss the relation of the polynomiality property of the solutions of the Q-system in the initial variables, which follows from the representation-theoretical interpretation, to the Laurent phenomenon in cluster algebras (Fomin and Zelevinsky 2002 Adv. Appl. Math. 28 119-44)

  5. Waterloo Workshop on Computer Algebra

    CERN Document Server

    Zima, Eugene; WWCA-2016; Advances in computer algebra : in honour of Sergei Abramov's' 70th birthday

    2018-01-01

    This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016.   This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

  6. The Cuntz algebra Q_N and C*-algebras of product systems

    DEFF Research Database (Denmark)

    Hong, Jeong Hee; Larsen, Nadia S.; Szymanski, Wojciech

    2011-01-01

    We consider a product system over the multiplicative group semigroup N^x of Hilbert bimodules which is implicit in work of S. Yamashita and of the second named author. We prove directly, using universal properties, that the associated Nica-Toeplitz algebra is an extension of the C*-algebra Q...

  7. Lectures on algebraic quantum field theory and operator algebras

    International Nuclear Information System (INIS)

    Schroer, Bert

    2001-04-01

    In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as why mathematicians are/should be interested in algebraic quantum field theory would be equally fitting. besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical. (author)

  8. q-deformations of noncompact Lie (super-) algebras: The examples of q-deformed Lorentz, Weyl, Poincare' and (super-) conformal algebras

    International Nuclear Information System (INIS)

    Dobrev, V.K.

    1992-01-01

    We review and explain a canonical procedure for the q-deformation of the real forms G of complex Lie (super-) algebras associated with (generalized) Cartan matrices. Our procedure gives different q-deformations for the non-conjugate Cartan subalgebras of G. We give several in detail the q-deformed Lorentz and conformal (super-) algebras. The q-deformed conformal algebra contains as a subalgebra a q-deformed Poincare algebra and as Hopf subalgebras two conjugate 11-generator q-deformed Weyl algebras. The q-deformed Lorentz algebra in Hopf subalgebra of both Weyl algebras. (author). 24 refs

  9. Assessing Algebraic Solving Ability: A Theoretical Framework

    Science.gov (United States)

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  10. Associative and Lie deformations of Poisson algebras

    OpenAIRE

    Remm, Elisabeth

    2011-01-01

    Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations which preserves the underlying associative structure and we study deformations which preserve the underlying Lie algebra.

  11. Paragrassmann analysis and covariant quantum algebras

    International Nuclear Information System (INIS)

    Filippov, A.T.; Isaev, A.P.; Kurdikov, A.B.; Pyatov, P.N.

    1993-01-01

    This report is devoted to the consideration from the algebraic point of view the paragrassmann algebras with one and many paragrassmann generators Θ i , Θ p+1 i = 0. We construct the paragrassmann versions of the Heisenberg algebra. For the special case, this algebra is nothing but the algebra for coordinates and derivatives considered in the context of covariant differential calculus on quantum hyperplane. The parameter of deformation q in our case is (p+1)-root of unity. Our construction is nondegenerate only for even p. Taking bilinear combinations of paragrassmann derivatives and coordinates we realize generators for the covariant quantum algebras as tensor products of (p+1) x (p+1) matrices. (orig./HSI)

  12. Arylation of beta, gamma-unsaturated lactones by a Heck-Matsuda reaction: an unexpected route to aryldiazene butenolides and pyridazinones

    Energy Technology Data Exchange (ETDEWEB)

    Taylor, Jason G.; Correia, Carlos Roque D., E-mail: roque@iqm.unicamp.b [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Inst. de Quimica

    2010-07-01

    The palladium catalysed coupling of aryldiazonium salts with {beta}-{gamma}-unsaturated lactones under basic conditions has been investigated. Both (3H)-furanone and {alpha}-angelicalactone were evaluated as substrates in the Heck Matsuda reaction but both failed to afford the desired arylated butenolides. Under basic conditions, {beta}-{gamma}-unsaturated lactones generate highly nucleophilic enolates that preferentially undergo azo coupling reactions with arenediazonium salts to afford aryldiazene butenolides. The electronic and steric effect of the substituents on the aryldiazonium salt in the azo coupling reaction is described. Aryldiazene-lactone derivatives were obtained in good yields from a highly facile and straightforward procedure. An aminoisomaleimide was formed from (3H)-furanone and cyclized to the corresponding pyridazinones in modest yield. (author)

  13. CLASSIFICATION OF 4-DIMENSIONAL GRADED ALGEBRAS

    OpenAIRE

    Armour, Aaron; Chen, Hui-Xiang; ZHANG, Yinhuo

    2009-01-01

    Let k be an algebraically closed field. The algebraic and geometric classification of finite dimensional algebras over k with ch(k) not equal 2 was initiated by Gabriel in [6], where a complete list of nonisomorphic 4-dimensional k-algebras was given and the number of irreducible components of the variety Alg(4) was discovered to be 5. The classification of 5-dimensional k-algebras was done by Mazzola in [10]. The number of irreducible components of the variety Alg(5) is 10. With the dimensio...

  14. Banana Algebra: Compositional syntactic language extension

    DEFF Research Database (Denmark)

    Andersen, Jacob; Brabrand, Claus; Christiansen, David Raymond

    2013-01-01

    We propose an algebra of languages and transformations as a means of compositional syntactic language extension. The algebra provides a layer of high-level abstractions built on top of languages (captured by context-free grammars) and transformations (captured by constructive catamorphisms...... algebra as presented in the paper is implemented as the Banana Algebra Tool which may be used to syntactically extend languages in an incremental and modular fashion via algebraic composition of previously defined languages and transformations. We demonstrate and evaluate the tool via several kinds...

  15. Linear algebra

    CERN Document Server

    Liesen, Jörg

    2015-01-01

    This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

  16. JB*-Algebras of Topological Stable Rank 1

    Directory of Open Access Journals (Sweden)

    Akhlaq A. Siddiqui

    2007-01-01

    Full Text Available In 1976, Kaplansky introduced the class JB*-algebras which includes all C*-algebras as a proper subclass. The notion of topological stable rank 1 for C*-algebras was originally introduced by M. A. Rieffel and was extensively studied by various authors. In this paper, we extend this notion to general JB*-algebras. We show that the complex spin factors are of tsr 1 providing an example of special JBW*-algebras for which the enveloping von Neumann algebras may not be of tsr 1. In the sequel, we prove that every invertible element of a JB*-algebra is positive in certain isotope of ; if the algebra is finite-dimensional, then it is of tsr 1 and every element of is positive in some unitary isotope of . Further, it is established that extreme points of the unit ball sufficiently close to invertible elements in a JB*-algebra must be unitaries and that in any JB*-algebras of tsr 1, all extreme points of the unit ball are unitaries. In the end, we prove the coincidence between the λ-function and λu-function on invertibles in a JB*-algebra.

  17. (Super)conformal algebra on the (super)torus

    International Nuclear Information System (INIS)

    Mezincescu, L.; Nepomechie, R.I.; Zachos, C.K.

    1989-01-01

    A generalization of the Virasoro algebra has recently been introduced by Krichever and Novikov (KN). The KN algebra describes the algebra of general conformal transformations in a basis appropriate to a genus-g Riemann surface. We examine in detail the genus-one KN algebra, and find explicit expressions for the central extension. We, further, construct explicitly the superconformal algebra of the supertorus, which yields supersymmetric generalizations of the genus-one KN algebra. A novel feature of the odd-spin-structure case is that the algebra includes a central element which is anticommuting. We comment on possible applications to string theory. (orig.)

  18. Spin-4 extended conformal algebras

    International Nuclear Information System (INIS)

    Kakas, A.C.

    1988-01-01

    We construct spin-4 extended conformal algebras using the second hamiltonian structure of the KdV hierarchy. In the presence of a U(1) current a family of spin-4 algebras exists but the additional requirement that the spin-1 and spin-4 currents commute fixes the algebra uniquely. (orig.)

  19. Computer algebra applications

    International Nuclear Information System (INIS)

    Calmet, J.

    1982-01-01

    A survey of applications based either on fundamental algorithms in computer algebra or on the use of a computer algebra system is presented. Recent work in biology, chemistry, physics, mathematics and computer science is discussed. In particular, applications in high energy physics (quantum electrodynamics), celestial mechanics and general relativity are reviewed. (Auth.)

  20. Nonlinear evolution equations and solving algebraic systems: the importance of computer algebra

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Kostov, N.A.

    1989-01-01

    In the present paper we study the application of computer algebra to solve the nonlinear polynomial systems which arise in investigation of nonlinear evolution equations. We consider several systems which are obtained in classification of integrable nonlinear evolution equations with uniform rank. Other polynomial systems are related with the finding of algebraic curves for finite-gap elliptic potentials of Lame type and generalizations. All systems under consideration are solved using the method based on construction of the Groebner basis for corresponding polynomial ideals. The computations have been carried out using computer algebra systems. 20 refs

  1. Filiform Lie algebras of order 3

    Science.gov (United States)

    Navarro, R. M.

    2014-04-01

    The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, "Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes," Bull. Soc. Math. France 98, 81-116 (1970)]. Also we give the dimension, using an adaptation of the {sl}(2,{C})-module Method, and a basis of such infinitesimal deformations in some generic cases.

  2. Rudiments of algebraic geometry

    CERN Document Server

    Jenner, WE

    2017-01-01

    Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

  3. Applications of Computer Algebra Conference

    CERN Document Server

    Martínez-Moro, Edgar

    2017-01-01

    The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.

  4. Chiral algebras of class S

    CERN Document Server

    Beem, Christopher; Rastelli, Leonardo; van Rees, Balt C.

    2015-01-01

    Four-dimensional N=2 superconformal field theories have families of protected correlation functions that possess the structure of two-dimensional chiral algebras. In this paper, we explore the chiral algebras that arise in this manner in the context of theories of class S. The class S duality web implies nontrivial associativity properties for the corresponding chiral algebras, the structure of which is best summarized in the language of generalized topological quantum field theory. We make a number of conjectures regarding the chiral algebras associated to various strongly coupled fixed points.

  5. Homotopy Theory of C*-Algebras

    CERN Document Server

    Ostvaer, Paul Arne

    2010-01-01

    Homotopy theory and C* algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It

  6. Computational aspects of algebraic curves

    CERN Document Server

    Shaska, Tanush

    2005-01-01

    The development of new computational techniques and better computing power has made it possible to attack some classical problems of algebraic geometry. The main goal of this book is to highlight such computational techniques related to algebraic curves. The area of research in algebraic curves is receiving more interest not only from the mathematics community, but also from engineers and computer scientists, because of the importance of algebraic curves in applications including cryptography, coding theory, error-correcting codes, digital imaging, computer vision, and many more.This book cove

  7. The algebras of large N matrix mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Halpern, M.B.; Schwartz, C.

    1999-09-16

    Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

  8. (L,M-Fuzzy σ-Algebras

    Directory of Open Access Journals (Sweden)

    Fu-Gui Shi

    2010-01-01

    Full Text Available The notion of (L,M-fuzzy σ-algebras is introduced in the lattice value fuzzy set theory. It is a generalization of Klement's fuzzy σ-algebras. In our definition of (L,M-fuzzy σ-algebras, each L-fuzzy subset can be regarded as an L-measurable set to some degree.

  9. Explicit field realizations of W algebras

    OpenAIRE

    Wei, Shao-Wen; Liu, Yu-Xiao; Zhang, Li-Jie; Ren, Ji-Rong

    2009-01-01

    The fact that certain non-linear $W_{2,s}$ algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize $W_{2,s}$ algebras from linear $W_{1,2,s}$ algebras. In this paper, we first construct the explicit field realizations of linear $W_{1,2,s}$ algebras with double-scalar and double-spinor, respectively. Then, after a change of basis, the realizations of $W_{2,s}$ algebras are presented. The results show that all these realizations are Romans-type realiz...

  10. Explicit field realizations of W algebras

    International Nuclear Information System (INIS)

    Wei Shaowen; Liu Yuxiao; Ren Jirong; Zhang Lijie

    2009-01-01

    The fact that certain nonlinear W 2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W 2,s algebras from linear W 1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W 1,2,s algebras with double scalar and double spinor, respectively. Then, after a change of basis, the realizations of W 2,s algebras are presented. The results show that all these realizations are Romans-type realizations.

  11. Hurwitz Algebras and the Octonion Algebra

    Science.gov (United States)

    Burdik, Čestmir; Catto, Sultan

    2018-02-01

    We explore some consequences of a theory of internal symmetries for elementary particles constructed on exceptional quantum mechanical spaces based on Jordan algebra formulation that admit exceptional groups as gauge groups.

  12. On d -Dimensional Lattice (co)sine n -Algebra

    International Nuclear Information System (INIS)

    Yao Shao-Kui; Zhang Chun-Hong; Zhao Wei-Zhong; Ding Lu; Liu Peng

    2016-01-01

    We present the (co)sine n-algebra which is indexed by the d-dimensional integer lattice. Due to the associative operators, this generalized (co)sine n-algebra is the higher order Lie algebra for the n even case. The particular cases are the d-dimensional lattice sine 3 and cosine 5-algebras with the special parameter values. We find that the corresponding d-dimensional lattice sine 3 and cosine 5-algebras are the Nambu 3-algebra and higher order Lie algebra, respectively. The limiting case of the d-dimensional lattice (co)sine n-algebra is also discussed. Moreover we construct the super sine n-algebra, which is the super higher order Lie algebra for the n even case. (paper)

  13. Pre-Algebra Lexicon.

    Science.gov (United States)

    Hayden, Dunstan; Cuevas, Gilberto

    The pre-algebra lexicon is a set of classroom exercises designed to teach the technical words and phrases of pre-algebra mathematics, and includes the terms most commonly found in related mathematics courses. The lexicon has three parts, each with its own introduction. The first introduces vocabulary items in three groups forming a learning…

  14. An Arithmetic-Algebraic Work Space for the Promotion of Arithmetic and Algebraic Thinking: Triangular Numbers

    Science.gov (United States)

    Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos

    2016-01-01

    This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…

  15. n-ary algebras: a review with applications

    International Nuclear Information System (INIS)

    De Azcarraga, J A; Izquierdo, J M

    2010-01-01

    This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. 3-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. As a result, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations (it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A 4 model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization. (topical

  16. Additive derivations on algebras of measurable operators

    International Nuclear Information System (INIS)

    Ayupov, Sh.A.; Kudaybergenov, K.K.

    2009-08-01

    Given a von Neumann algebra M we introduce the so-called central extension mix(M) of M. We show that mix(M) is a *-subalgebra in the algebra LS(M) of all locally measurable operators with respect to M, and this algebra coincides with LS(M) if and only if M does not admit type II direct summands. We prove that if M is a properly infinite von Neumann algebra then every additive derivation on the algebra mix(M) is inner. This implies that on the algebra LS(M), where M is a type I ∞ or a type III von Neumann algebra, all additive derivations are inner derivations. (author)

  17. Families talen en algebra

    NARCIS (Netherlands)

    Asveld, P.R.J.

    1976-01-01

    Operaties op formele talen geven aanleiding tot bijbehorende operatoren op families talen. Bepaalde onderwerpen uit de algebra (universele algebra, tralies, partieel geordende monoiden) kunnen behulpzaam zijn in de studie van verzamelingen van dergelijke operatoren.

  18. Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

    International Nuclear Information System (INIS)

    Ammar, F; Makhlouf, A; Silvestrov, S

    2010-01-01

    In this paper we construct ternary q-Virasoro-Witt algebras which q-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using su(1, 1) enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary q-Virasoro-Witt algebras constructed in this paper are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield a Hom-Nambu-Lie algebra structure for q-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary q-Virasoro-Witt algebras we construct, carry a structure of the ternary Hom-Nambu-Lie algebra for all values of the involved parameters.

  19. Algebraic Methods to Design Signals

    Science.gov (United States)

    2015-08-27

    to date on designing signals using algebraic and combinatorial methods. Mathematical tools from algebraic number theory, representation theory and... combinatorial objects in designing signals for communication purposes. Sequences and arrays with desirable autocorrelation properties have many...multiple access methods in mobile radio communication systems. We continue our mathematical framework based on group algebras, character theory

  20. Assessing Elementary Algebra with STACK

    Science.gov (United States)

    Sangwin, Christopher J.

    2007-01-01

    This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

  1. Homological methods, representation theory, and cluster algebras

    CERN Document Server

    Trepode, Sonia

    2018-01-01

    This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, wh...

  2. From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets

    OpenAIRE

    Jurco, Branislav

    2011-01-01

    Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, which is simply connected in each simplicial level. We use the 1-jet of the classifying space of G to construct, starting from g, a Lie k-algebra L. The so constructed Lie k-algebra L is actually a differential graded Lie algebra. The differential and the brackets are explicitly described in terms (of a part) of the corresponding k-hypercrossed complex structure of Ng. The res...

  3. Classification and identification of Lie algebras

    CERN Document Server

    Snobl, Libor

    2014-01-01

    The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain cl...

  4. Sugawara operators for classical Lie algebras

    CERN Document Server

    Molev, Alexander

    2018-01-01

    The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical \\mathcal{W}-algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connec...

  5. Filiform Lie algebras of order 3

    International Nuclear Information System (INIS)

    Navarro, R. M.

    2014-01-01

    The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases

  6. Algebraic Systems and Pushdown Automata

    Science.gov (United States)

    Petre, Ion; Salomaa, Arto

    We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.

  7. Ready, Set, Algebra?

    Science.gov (United States)

    Levy, Alissa Beth

    2012-01-01

    The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this dissertation,…

  8. Block diagonalization for algebra's associated with block codes

    NARCIS (Netherlands)

    D. Gijswijt (Dion)

    2009-01-01

    htmlabstractFor a matrix *-algebra B, consider the matrix *-algebra A consisting of the symmetric tensors in the n-fold tensor product of B. Examples of such algebras in coding theory include the Bose-Mesner algebra and Terwilliger algebra of the (non)binary Hamming cube, and algebras arising in

  9. Grassmann, super-Kac-Moody and super-derivation algebras

    International Nuclear Information System (INIS)

    Frappat, L.; Ragoucy, E.; Sorba, P.

    1989-05-01

    We study the cyclic cocycles of degree one on the Grassmann algebra and on the super-circle with N supersymmetries (i.e. the tensor product of the algebra of functions on the circle times a Grassmann algebra with N generators). They are related to central extensions of graded loop algebras (i.e. super-Kac-Moody algebras). The corresponding algebras of super-derivations have to be compatible with the cocycle characterizing the extension; we give a general method for determining these algebras and examine in particular the cases N = 1,2,3. We also discuss their relations with the Ademollo et al. algebras, and examine the possibility of defining new kinds of super-conformal algebras, which, for N > 1, generalize the N = 1 Ramond-Neveu-Schwarz algebra

  10. Current algebra

    International Nuclear Information System (INIS)

    Jacob, M.

    1967-01-01

    The first three chapters of these lecture notes are devoted to generalities concerning current algebra. The weak currents are defined, and their main properties given (V-A hypothesis, conserved vector current, selection rules, partially conserved axial current,...). The SU (3) x SU (3) algebra of Gell-Mann is introduced, and the general properties of the non-leptonic weak Hamiltonian are discussed. Chapters 4 to 9 are devoted to some important applications of the algebra. First one proves the Adler- Weisberger formula, in two different ways, by either the infinite momentum frame, or the near-by singularities method. In the others chapters, the latter method is the only one used. The following topics are successively dealt with: semi leptonic decays of K mesons and hyperons, Kroll- Ruderman theorem, non leptonic decays of K mesons and hyperons ( ΔI = 1/2 rule), low energy theorems concerning processes with emission (or absorption) of a pion or a photon, super-convergence sum rules, and finally, neutrino reactions. (author) [fr

  11. Linear algebra

    CERN Document Server

    Edwards, Harold M

    1995-01-01

    In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject

  12. A type of loop algebra and the associated loop algebras

    International Nuclear Information System (INIS)

    Tam Honwah; Zhang Yufeng

    2008-01-01

    A higher-dimensional twisted loop algebra is constructed. As its application, a new Lax pair is presented, whose compatibility gives rise to a Liouville integrable hierarchy of evolution equations by making use of Tu scheme. One of the reduction cases of the hierarchy is an analogous of the well-known AKNS system. Next, the twisted loop algebra, furthermore, is extended to another higher dimensional loop algebra, from which a hierarchy of evolution equations with 11-potential component functions is obtained, whose reduction is just standard AKNS system. Especially, we prove that an arbitrary linear combination of the four Hamiltonian operators directly obtained from the recurrence relations is still a Hamiltonian operator. Therefore, the hierarchy with 11-potential functions possesses 4-Hamiltonian structures. Finally, an integrable coupling of the hierarchy is worked out

  13. Spin-zero mesons and current algebras

    International Nuclear Information System (INIS)

    Wellner, M.

    1977-01-01

    Large chiral algebras, using the f and d coefficients of SU(3) can be constructed with spin-1/2 baryons. Such algebras have been found useful in some previous investigations. This article examines under what conditions similar or identical current algebras may be realized with spin-0 mesons. A curious lack of analogy emerges between meson and baryon currents. Second-class currents, made of mesons, are required in some algebras. If meson and baryon currents are to satisfy the same extended SU(3) algebra, four meson nonets are needed, in terms of which we give an explicit construction for the currents

  14. Chiral algebras for trinion theories

    International Nuclear Information System (INIS)

    Lemos, Madalena; Peelaers, Wolfger

    2015-01-01

    It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T n theories. The conjecture is motivated by making manifest the critical affine module structure in the graded partition function of the chiral algebras, which is computed by the Schur limit of the superconformal index for T n theories. We also explicitly construct the chiral algebra arising from the T 4 theory. Its null relations give rise to new T 4 Higgs branch chiral ring relations.

  15. The $W_{3}$ algebra modules, semi-infinite cohomology and BV algebras

    CERN Document Server

    Bouwknegt, Peter; Pilch, Krzysztof

    1996-01-01

    The noncritical D=4 W_3 string is a model of W_3 gravity coupled to two free scalar fields. In this paper we discuss its BRST quantization in direct analogy with that of the D=2 (Virasoro) string. In particular, we calculate the physical spectrum as a problem in BRST cohomology. The corresponding operator cohomology forms a BV-algebra. We model this BV-algebra on that of the polyderivations of a commutative ring on six variables with a quadratic constraint, or equivalently, on the BV-algebra of (polynomial) polyvector fields on the base affine space of SL(3,C). In this paper we attempt to present a complete summary of the progress made in these studies. [...

  16. Normed algebras and the geometric series test

    Directory of Open Access Journals (Sweden)

    Robert Kantrowitz

    2017-11-01

    Full Text Available The purpose of this article is to survey a class of normed algebras that share many central features of Banach algebras, save for completeness. The likeness of these algebras to Banach algebras derives from the fact that the geometric series test is valid, whereas the lack of completeness points to the failure of the absolute convergence test for series in the algebra. Our main result is a compendium of conditions that are all equivalent to the validity of the geometric series test for commutative unital normed algebras. Several examples in the final section showcase some incomplete normed algebras for which the geometric series test is valid, and still others for which it is not.

  17. A modal characterization of Peirce algebras

    NARCIS (Netherlands)

    M. de Rijke (Maarten)

    1995-01-01

    textabstractPeirce algebras combine sets, relations and various operations linking the two in a unifying setting.This note offers a modal perspective on Peirce algebras.It uses modal logic to characterize the full Peirce algebras.

  18. On δ-derivations of n-ary algebras

    International Nuclear Information System (INIS)

    Kaygorodov, Ivan B

    2012-01-01

    We give a description of δ-derivations of (n+1)-dimensional n-ary Filippov algebras and, as a consequence, of simple finite-dimensional Filippov algebras over an algebraically closed field of characteristic zero. We also give new examples of non-trivial δ-derivations of Filippov algebras and show that there are no non-trivial δ-derivations of the simple ternary Mal'tsev algebra M 8 .

  19. Sub-subleading soft gravitons and large diffeomorphisms

    Energy Technology Data Exchange (ETDEWEB)

    Campiglia, Miguel [Instituto de Física, Facultad de Ciencias,Montevideo 11400 (Uruguay); Laddha, Alok [Chennai Mathematical Institute,Siruseri 603103 (India)

    2017-01-10

    We present strong evidence that the sub-subleading soft theorem in semi-classical (tree level) gravity discovered by Cachazo and Strominger is equivalent to the conservation of asymptotic charges associated to a new class of vector fields not contained within the previous extensions of BMS algebra. Our analysis crucially relies on analyzing the hitherto established equivalences between soft theorems and Ward identities from a new perspective. In this process we naturally (re)discover a class of ‘magnetic’ charges at null infinity that are associated to the dual of the Weyl tensor.

  20. Cluster algebras in mathematical physics

    International Nuclear Information System (INIS)

    Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

    2014-01-01

    This special issue of Journal of Physics A: Mathematical and Theoretical contains reviews and original research articles on cluster algebras and their applications to mathematical physics. Cluster algebras were introduced by S Fomin and A Zelevinsky around 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. Since then the theory has found diverse applications in mathematics and mathematical physics. Cluster algebras are axiomatically defined commutative rings equipped with a distinguished set of generators (cluster variables) subdivided into overlapping subsets (clusters) of the same cardinality subject to certain polynomial relations. A cluster algebra of rank n can be viewed as a subring of the field of rational functions in n variables. Rather than being presented, at the outset, by a complete set of generators and relations, it is constructed from the initial seed via an iterative procedure called mutation producing new seeds successively to generate the whole algebra. A seed consists of an n-tuple of rational functions called cluster variables and an exchange matrix controlling the mutation. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker and Ptolemy relations, Stokes curves and wall-crossing phenomena, Feynman integrals, Somos sequences and Hirota equations to name just a few examples). The cluster variables enjoy a remarkable combinatorial pattern; in particular, they exhibit the Laurent phenomenon: they are expressed as Laurent polynomials rather than more general rational functions in terms of the cluster variables in any seed. These characteristic features are often referred to as the cluster algebra structure. In the last decade, it became apparent that cluster structures are ubiquitous in mathematical physics. Examples include supersymmetric gauge theories, Poisson geometry, integrable systems, statistical mechanics, fusion products in infinite dimensional algebras, dilogarithm

  1. The central extensions of Kac-Moody-Malcev algebras

    International Nuclear Information System (INIS)

    Osipov, E.P.

    1989-01-01

    The authors introduce a class of infinite-dimensional Kac-Moody-Malcev algebras. The Kac-Moody-Malcev algebras are the generalization of Lie algebras of Kac-Moody type to the Malcev algebras. They demonstrate that the central extensions of Kac-Moody-Malcev algebras are given by the same cocycles as in the case of Lie algebras. It is given a construction of Virasoro algebra in terms of bilinear combinations of currents satisfying the Kac-Moody-Malcev commutation relations. Thus, it is given the generalization of the Sugawara Construction to the case of Kac-Moody-Malcev algebras. Analogues of Kac-Moody-Malcev algebras may be also introduced in the case of arbitrary Riemann surface

  2. Using Max-Plus Algebra for the Evaluation of Stochastic Process Algebra Prefixes

    NARCIS (Netherlands)

    Cloth, L.; de Alfaro, L.; Gilmore, S.; Bohnenkamp, H.C.; Haverkort, Boudewijn R.H.M.

    2001-01-01

    In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an

  3. The structure of relation algebras generated by relativizations

    CERN Document Server

    Givant, Steven R

    1994-01-01

    The foundation for an algebraic theory of binary relations was laid by De Morgan, Peirce, and Schröder during the second half of the nineteenth century. Modern development of the subject as a theory of abstract algebras, called "relation algebras", was undertaken by Tarski and his students. This book aims to analyze the structure of relation algebras that are generated by relativized subalgebras. As examples of their potential for applications, the main results are used to establish representation theorems for classes of relation algebras and to prove existence and uniqueness theorems for simple closures (i.e., for minimal simple algebras containing a given family of relation algebras as relativized subalgebras). This book is well written and accessible to those who are not specialists in this area. In particular, it contains two introductory chapters on the arithmetic and the algebraic theory of relation algebras. This book is suitable for use in graduate courses on algebras of binary relations or algebraic...

  4. Linear-Algebra Programs

    Science.gov (United States)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  5. P-commutative topological *-algebras

    International Nuclear Information System (INIS)

    Mohammad, N.; Thaheem, A.B.

    1991-07-01

    If P(A) denotes the set of all continuous positive functionals on a unital complete Imc *-algebra and S(A) the extreme points of P(A), and if the spectrum of an element χ Ε A coincides with the set {f(χ): f Ε S(A)}, then A is shown to be P-commutative. Moreover, if A is unital symmetric Frechet Q Imc *-algebra, then this spectral condition is, in fact, necessary. Also, an isomorphism theorem between symmetric Frechet P-commutative Imc *-algebras is established. (author). 12 refs

  6. Matrices and linear algebra

    CERN Document Server

    Schneider, Hans

    1989-01-01

    Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t

  7. Generalized NLS hierarchies from rational W algebras

    International Nuclear Information System (INIS)

    Toppan, F.

    1993-11-01

    Finite rational W algebras are very natural structures appearing in coset constructions when a Kac-Moody subalgebra is factored out. The problem of relating these algebras to integrable hierarchies of equations is studied by showing how to associate to a rational W algebra its corresponding hierarchy. Two examples are worked out, the sl(2)/U(1) coset, leading to the Non-Linear Schroedinger hierarchy, and the U(1) coset of the Polyakov-Bershadsky W algebra, leading to a 3-field representation of the KP hierarchy already encountered in the literature. In such examples a rational algebra appears as algebra of constraints when reducing a KP hierarchy to a finite field representation. This fact arises the natural question whether rational algebras are always associated to such reductions and whether a classification of rational algebras can lead to a classification of the integrable hierarchies. (author). 19 refs

  8. Some Aspects of -Units in BCK-Algebras

    Directory of Open Access Journals (Sweden)

    Hee Sik Kim

    2012-01-01

    Full Text Available We explore properties of the set of d-units of a -algebra. A property of interest in the study of -units in -algebras is the weak associative property. It is noted that many other -algebras, especially -algebras, are in fact weakly associative. The existence of -algebras which are not weakly associative is demonstrated. Moreover, the notions of a -integral domain and a left-injectivity are discussed.

  9. Bases in Lie and quantum algebras

    International Nuclear Information System (INIS)

    Ballesteros, A; Celeghini, E; Olmo, M A del

    2008-01-01

    Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we have not enough primitive elements that allow for a privileged set of generators and all basic sets are equivalent. In this paper we discuss how the Drinfeld double structure underlying every simple Lie bialgebra characterizes uniquely a particular basis without any freedom, completing the Cartan program on simple algebras. By means of a perturbative construction, a distinguished deformed basis (we call it the analytical basis) is obtained for every quantum group as the analytical prolongation of the above defined Lie basis of the corresponding Lie bialgebra. It turns out that the whole construction is unique, so to each quantum universal enveloping algebra is associated one and only one bialgebra. In this way the problem of the classification of quantum algebras is moved to the classification of bialgebras. In order to make this procedure more clear, we discuss in detail the simple cases of su(2) and su q (2).

  10. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

  11. On Deformations and Contractions of Lie Algebras

    Directory of Open Access Journals (Sweden)

    Marc de Montigny

    2006-05-01

    Full Text Available In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras. We first discuss low-dimensional Lie algebras and illustrate thereby that whereas for every contraction there exists a reverse deformation, the converse is not true in general. Also we note that some Lie algebras belonging to parameterized families are singled out by the irreversibility of deformations and contractions. After reminding that global deformations of the Witt, Virasoro, and affine Kac-Moody algebras allow one to retrieve Lie algebras of Krichever-Novikov type, we contract the latter to find new infinite dimensional Lie algebras.

  12. Algebraic Description of Motion

    Science.gov (United States)

    Davidon, William C.

    1974-01-01

    An algebraic definition of time differentiation is presented and used to relate independent measurements of position and velocity. With this, students can grasp certain essential physical, geometric, and algebraic properties of motion and differentiation before undertaking the study of limits. (Author)

  13. Black Hole Entropy from Bondi-Metzner-Sachs Symmetry at the Horizon.

    Science.gov (United States)

    Carlip, S

    2018-03-09

    Near the horizon, the obvious symmetries of a black hole spacetime-the horizon-preserving diffeomorphisms-are enhanced to a larger symmetry group with a three-dimensional Bondi-Metzner-Sachs algebra. Using dimensional reduction and covariant phase space techniques, I investigate this augmented symmetry and show that it is strong enough to determine the black hole entropy in any dimension.

  14. Deformation of the exterior algebra and the GLq (r, included in) algebra

    International Nuclear Information System (INIS)

    El Hassouni, A.; Hassouni, Y.; Zakkari, M.

    1993-06-01

    The deformation of the associative algebra of exterior forms is performed. This operation leads to a Y.B. equation. Its relation with the braid group B n-1 is analyzed. The correspondence of this deformation with the GL q (r, included in) algebra is developed. (author). 9 refs

  15. A lecture on the Calogero-Sutherland models

    International Nuclear Information System (INIS)

    Pasquier, V.

    1994-01-01

    In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shatry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics. The form factor of the density operator. 2) The Dunkl operators and their relations with monodromy matrices, Yangians and affine-Hecke algebras. 3) The Haldane-Shastry chain in connection with the Calogero-Sutherland Hamiltonian at a specific coupling constant. (orig.)

  16. The Universal Askey-Wilson Algebra

    Directory of Open Access Journals (Sweden)

    Paul Terwilliger

    2011-07-01

    Full Text Available In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3 and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension Δ of AW, obtained from AW by reinterpreting certain parameters as central elements in the algebra. We call Δ the universal Askey-Wilson algebra. We give a faithful action of the modular group PSL_2(Z on Δ as a group of automorphisms. We give a linear basis for Δ. We describe the center of Δ and the 2-sided ideal Δ[Δ,Δ]Δ. We discuss how Δ is related to the q-Onsager algebra.

  17. Linear algebra

    CERN Document Server

    Stoll, R R

    1968-01-01

    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand

  18. Lie algebras

    CERN Document Server

    Jacobson, Nathan

    1979-01-01

    Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its

  19. Basic algebra

    CERN Document Server

    Jacobson, Nathan

    2009-01-01

    A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as L

  20. Feature-Oriented Programming with Object Algebras

    NARCIS (Netherlands)

    B.C.d.S. Oliveira (Bruno); T. van der Storm (Tijs); A. Loh; W.R. Cook

    2013-01-01

    htmlabstractObject algebras are a new programming technique that enables a simple solution to basic extensibility and modularity issues in programming languages. While object algebras excel at defining modular features, the composition mechanisms for object algebras (and features) are still

  1. Representations of fundamental groups of algebraic varieties

    CERN Document Server

    Zuo, Kang

    1999-01-01

    Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.

  2. Located actions in process algebra with timing

    NARCIS (Netherlands)

    Bergstra, J.A.; Middelburg, C.A.

    2004-01-01

    We propose a process algebra obtained by adapting the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, 2002, Chap. 4] to spatially located actions. This process algebra makes it possible to deal with the behaviour of systems with a

  3. Lie Algebras Associated with Group U(n)

    International Nuclear Information System (INIS)

    Zhang Yufeng; Dong Huanghe; Honwah Tam

    2007-01-01

    Starting from the subgroups of the group U(n), the corresponding Lie algebras of the Lie algebra A 1 are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras are classified into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given.

  4. Synthesis and characterization of para-pyridine linked NHC palladium complexes and their studies for the Heck-Mizoroki coupling reaction.

    Science.gov (United States)

    Liu, Ya-Ming; Lin, Yi-Chun; Chen, Wen-Ching; Cheng, Jen-Hao; Chen, Yi-Lin; Yap, Glenn P A; Sun, Shih-Sheng; Ong, Tiow-Gan

    2012-06-28

    This paper describes the synthesis of 1-(pyridine-4-ylmethyl) NHC and their Pd(II) and Ag(I) complexes, which are fully characterized. Interestingly, we have also synthesized a Pd complex 3a-CO(3) using a more direct treatment of K(2)CO(3) with PdCl(2). 3a-CO(3) represents the first reported solid structure of a Pd η(2)-carbonato complex stabilized by an NHC framework. 3a-CO(3) can be easily converted to a PdCl(2) derivative by treating it with chloroform. We have found these palladium complexes mediate the Heck-Mizoroki coupling with a low catalyst loading. Furthermore, we also expand such catalytic manifold toward constructing fused polyaromatic substrates, a highly useful class of compounds in optoelectronic chemistry.

  5. Smarandache hyper BCC-algebra

    OpenAIRE

    Ahadpanah, A.; Borumand Saeid, A.

    2011-01-01

    In this paper, we define the Smarandache hyper BCC-algebra, and Smarandache hyper BCC-ideals of type 1, 2, 3 and 4. We state and prove some theorems in Smarandache hyper BCC -algebras, and then we determine the relationships between these hyper ideals.

  6. ASYS: a computer algebra package for analysis of nonlinear algebraic equations systems

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Khutornoj, N.V.

    1992-01-01

    A program package ASYS for analysis of nonlinear algebraic equations based on the Groebner basis technique is described. The package is written in REDUCE computer algebra language. It has special facilities to treat polynomial ideals of positive dimension, corresponding to algebraic systems with infinitely many solutions. Such systems can be transformed to an equivalent set of subsystems with reduced number of variables in completely automatic way. It often allows to construct the explicit form of a solution set in many problems of practical importance. Some examples and results of comparison with the standard Reduce package GROEBNER and special-purpose systems FELIX and A1PI are given. 21 refs.; 2 tabs

  7. The N=2 super-W3 algebra

    International Nuclear Information System (INIS)

    Romans, L.J.

    1992-01-01

    We present the complete structure of the N=2 super-W 3 algebra, a non-linear extended conformal algebra containing the usual N=2 superconformal algebra (with generators of spins 1, 3/2, 3/2 and 2) and a higher-spin multiplet of generators with spins 2, 5/2, 5/2 and 3. We investigate various sub-algebras and related algebras, and find necessary conditions upon possible unitary representations of the algebra. In particular, the central charge c is restricted to two discrete series, one ascending and one descending to a common accumulation point c=6. The results suggest that the algebra is realised in certain (compact or non-compact) Kazama-Suzuki coset models, including a c=9 model proposed by Bars based on SU(2, 1)/U(2). (orig.)

  8. Quantization and representation theory of finite W algebras

    International Nuclear Information System (INIS)

    Boer, J. de; Tjin, T.

    1993-01-01

    In this paper we study the finitely generated algebras underlying W algebras. These so called 'finite W algebras' are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings of sl 2 into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finite W algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finite W symmetry. In the second part we BRST quantize the finite W algebras. The BRST cohomoloy is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finite W algebras in one stroke. Examples are given. In the last part of the paper we study the representation theory of finite W algebras. It is shown, using a quantum inversion of the generalized Miura transformation, that the representations of finite W algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finite W algebras. (orig.)

  9. Finite W-algebras and intermediate statistics

    International Nuclear Information System (INIS)

    Barbarin, F.; Ragoucy, E.; Sorba, P.

    1995-01-01

    New realizations of finite W-algebras are constructed by relaxing the usual constraint conditions. Then finite W-algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d=1 case, it is natural to consider that the W-algebra framework is well adapted for a possible generalization of the anyon statistics. ((orig.))

  10. Quantized Matrix Algebras and Quantum Seeds

    DEFF Research Database (Denmark)

    Jakobsen, Hans Plesner; Pagani, Chiara

    2015-01-01

    We determine explicitly quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centres and block diagonal forms of these algebras. In the case where is an arbitrary root of unity, this further determines the degrees.......We determine explicitly quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centres and block diagonal forms of these algebras. In the case where is an arbitrary root of unity, this further determines the degrees....

  11. Simple Lie algebras and Dynkin diagrams

    International Nuclear Information System (INIS)

    Buccella, F.

    1983-01-01

    The following theorem is studied: in a simple Lie algebra of rank p there are p positive roots such that all the other n-3p/2 positive roots are linear combinations of them with integer non negative coefficients. Dykin diagrams are built by representing the simple roots with circles and drawing a junction between the roots. Five exceptional algebras are studied, focusing on triple junction algebra, angular momentum algebra, weights of the representation, antisymmetric tensors, and subalgebras

  12. Algebra, Geometry and Mathematical Physics Conference

    CERN Document Server

    Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander

    2014-01-01

    This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...

  13. Basic algebraic topology and its applications

    CERN Document Server

    Adhikari, Mahima Ranjan

    2016-01-01

    This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. T...

  14. L_∞ algebras and field theory

    International Nuclear Information System (INIS)

    Hohm, Olaf; Zwiebach, Barton

    2017-01-01

    We review and develop the general properties of L_∞ algebras focusing on the gauge structure of the associated field theories. Motivated by the L_∞ homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L_∞ structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L_∞ algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L_∞ algebra for the interacting theory. The analysis suggests that L_∞ algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  15. Lie algebra of conformal Killing–Yano forms

    International Nuclear Information System (INIS)

    Ertem, Ümit

    2016-01-01

    We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing–Yano forms. A new Lie bracket for conformal Killing–Yano forms that corresponds to slightly modified Schouten–Nijenhuis bracket of differential forms is proposed. We show that conformal Killing–Yano forms satisfy a graded Lie algebra in constant curvature manifolds. It is also proven that normal conformal Killing–Yano forms in Einstein manifolds also satisfy a graded Lie algebra. The constructed graded Lie algebras reduce to the graded Lie algebra of Killing–Yano forms and the Lie algebras of conformal Killing and Killing vector fields in special cases. (paper)

  16. Constructing Meanings and Utilities within Algebraic Tasks

    Science.gov (United States)

    Ainley, Janet; Bills, Liz; Wilson, Kirsty

    2004-01-01

    The Purposeful Algebraic Activity project aims to explore the potential of spreadsheets in the introduction to algebra and algebraic thinking. We discuss two sub-themes within the project: tracing the development of pupils' construction of meaning for variable from arithmetic-based activity, through use of spreadsheets, and into formal algebra,…

  17. Algebraic groups and their birational invariants

    CERN Document Server

    Voskresenskiĭ, V E

    2011-01-01

    Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, R-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

  18. The classical limit of W-algebras

    International Nuclear Information System (INIS)

    Figueroa-O'Farrill, J.M.; Ramos, E.

    1992-01-01

    We define and compute explicitly the classical limit of the realizations of W n appearing as hamiltonian structures of generalized KdV hierarchies. The classical limit is obtained by taking the commutative limit of the ring of pseudodifferential operators. These algebras - denoted w n - have free field realizations in which the generators are given by the elementary symmetric polynomials in the free fields. We compute the algebras explicitly and we show that they are all reductions of a new algebra w KP , which is proposed as the universal classical W-algebra for the w n series. As a deformation of this algebra we also obtain w 1+∞ , the classical limit of W 1+∞ . (orig.)

  19. Higher regulators, algebraic

    CERN Document Server

    Bloch, Spencer J

    2000-01-01

    This book is the long-awaited publication of the famous Irvine lectures. Delivered in 1978 at the University of California at Irvine, these lectures turned out to be an entry point to several intimately-connected new branches of arithmetic algebraic geometry, such as regulators and special values of L-functions of algebraic varieties, explicit formulas for them in terms of polylogarithms, the theory of algebraic cycles, and eventually the general theory of mixed motives which unifies and underlies all of the above (and much more). In the 20 years since, the importance of Bloch's lectures has not diminished. A lucky group of people working in the above areas had the good fortune to possess a copy of old typewritten notes of these lectures. Now everyone can have their own copy of this classic work.

  20. Complex algebraic geometry

    CERN Document Server

    Kollár, János

    1997-01-01

    This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

  1. Basic algebraic geometry, v.2

    CERN Document Server

    Shafarevich, Igor Rostislavovich

    1994-01-01

    Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...

  2. Elements of algebraic coding systems

    CERN Document Server

    Cardoso da Rocha, Jr, Valdemar

    2014-01-01

    Elements of Algebraic Coding Systems is an introductory text to algebraic coding theory. In the first chapter, you'll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams' identities based on the probability of undetected error, and two important tools for algebraic decoding-namely, the finite field Fourier transform and the Euclidean algorithm f...

  3. Diamond lemma for the group graded quasi-algebras

    Indian Academy of Sciences (India)

    Introduction. The term quasi-algebra was introduced in [2] as an algebra in a monoidal category. Since the associativity constraints in these categories are allowed to be nontrivial, the class of quasi-algebras contains various important examples of non-associative algebras like the octonions and other Cayley algebras [2].

  4. The Centroid of a Lie Triple Algebra

    Directory of Open Access Journals (Sweden)

    Xiaohong Liu

    2013-01-01

    Full Text Available General results on the centroids of Lie triple algebras are developed. Centroids of the tensor product of a Lie triple algebra and a unitary commutative associative algebra are studied. Furthermore, the centroid of the tensor product of a simple Lie triple algebra and a polynomial ring is completely determined.

  5. The structure of the super-W∞(λ) algebra

    International Nuclear Information System (INIS)

    Bergshoeff, E.; Wit, B. de; Vasiliev, M.

    1991-01-01

    We give a comprehensive treatment of the super-W ∞ (λ) algebra, an extension of the super-Virasoro algebra that contains generators of spin S ≥ 1/2. The parameter λ defines the embedding of the Virasoro subalgebra. We describe how to obtain the super-W ∞ (λ) algebra from the associative algebra of superspace differential operators. We discuss the structure of this associative algebra and its relation with the so-called wedge algebra, in which the generators for given spin are restricted to finite-dimensional representations of sl(2). From the super-W ∞ (λ) algebra one can obtain a variety of W ∞ algebras by consistent truncations for specific values of λ. Without truncation the algebras are formally isomorphic for different values of λ. We present a realization in terms of the currents of a supersymmetric bc system. (orig.)

  6. Finite W-algebras and intermediate statistics

    International Nuclear Information System (INIS)

    Barbarin, F.; Ragoucy, E.; Sorba, P.

    1994-09-01

    New realizations of finite W-algebras are constructed by relaxing the usual conditions. Then finite W-algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d=1 case, it is natural to consider that the W-algebra framework is well adapted for a possible generalization of the anyon statistics. (author). 13 refs

  7. Asymptotic aspect of derivations in Banach algebras

    Directory of Open Access Journals (Sweden)

    Jaiok Roh

    2017-02-01

    Full Text Available Abstract We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.

  8. Algebraic characterizations of measure algebras

    Czech Academy of Sciences Publication Activity Database

    Jech, Thomas

    2008-01-01

    Roč. 136, č. 4 (2008), s. 1285-1294 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190509 Institutional research plan: CEZ:AV0Z10190503 Keywords : Von - Neumann * sequential topology * Boolean-algebras * Souslins problem * Submeasures Subject RIV: BA - General Mathematics Impact factor: 0.584, year: 2008

  9. Implementing the Standards: Teaching Informal Algebra.

    Science.gov (United States)

    Schultz, James E.

    1991-01-01

    Presents suggestions for developing algebraic concepts beginning in the early grades to develop a gradual building from informal to formal algebraic concepts that progresses over the K-12 curriculum. Includes suggestions for representing relationships, solving equations, employing meaningful applications of algebra, and using of technology. (MDH)

  10. Building bridges between algebra and topology

    CERN Document Server

    Pitsch, Wolfgang; Zarzuela, Santiago

    2018-01-01

    This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging Methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015. Homological algebra is a rich and ubiquitous subject; it is both an active field of research and a widespread toolbox for many mathematicians. Together, these notes introduce recent applications and interactions of homological methods in commutative algebra, representation theory and topology, narrowing the gap between specialists from different areas wishing to acquaint themselves with a rapidly growing field. The covered topics range from a fresh introduction to the growing area of support theory for triangulated categories to the striking consequences of the formulation in the homotopy theory of classical concepts in commutative algebra. Moreover, they also include a higher categories view of Hall algebras and an introduction to the use of idempotent functors in al...

  11. Summing Boolean Algebras

    Institute of Scientific and Technical Information of China (English)

    Antonio AIZPURU; Antonio GUTI(E)RREZ-D(A)VILA

    2004-01-01

    In this paper we will study some families and subalgebras ( ) of ( )(N) that let us characterize the unconditional convergence of series through the weak convergence of subseries ∑i∈A xi, A ∈ ( ).As a consequence, we obtain a new version of the Orlicz-Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.

  12. Quantum ergodicity and a quantum measure algebra

    International Nuclear Information System (INIS)

    Stechel, E.B.

    1985-01-01

    A quantum ergodic theory for finite systems (such as isolated molecules) is developed by introducing the concept of a quantum measure algebra. The basic concept in classical ergodic theory is that of a measure space. A measure space is a set M, together with a specified sigma algebra of subsets in M and a measure defined on that algebra. A sigma algebra is closed under the formation of intersections and symmetric differences. A measure is a nonnegative and countably additive set function. For this to be further classified as a dynamical system, a measurable transformation is introduced. A measurable transformation is a mapping from a measure space into a measure space, such that the inverse image of every measurable set is measurable. In conservative dynamical systems, a measurable transformation is measure preserving, which is to say that the inverse image of every measurable set has the same measure as the original set. Once the measure space and the measurable transformation are defined, ergodic theory can be investigated on three levels: describable as analytic, geometric and algebraic. The analytic level studies linear operators induced by a transformation. The geometric level is concerned directly with transformations on a measure space and the algebraic treatments substitute a measure algebra for the measure space and basically equate sets that differ only by sets of measure zero. It is this latter approach that is most directly paralleled here. A measure algebra for a quantum dynamical system is defined within which stochastic concepts in quantum mechanics can be investigated. The quantum measure algebra differs from a normal measure algebra only in that multiplication is noncommutative and addition is nonassociative. Nonetheless, the quantum measure algebra preserves the essence of a normal measure algebra

  13. The Leibniz-Hopf algebra and Lyndon words

    NARCIS (Netherlands)

    M. Hazewinkel (Michiel)

    1996-01-01

    textabstractLet ${cal Z$ denote the free associative algebra ${ol Z langle Z_1 , Z_2 , ldots rangle$ over the integers. This algebra carries a Hopf algebra structure for which the comultiplication is $Z_n mapsto Sigma_{i+j=n Z_i otimes Z_j$. This the noncommutative Leibniz-Hopf algebra. It carries a

  14. Strongly \\'etale difference algebras and Babbitt's decomposition

    OpenAIRE

    Tomašić, Ivan; Wibmer, Michael

    2015-01-01

    We introduce a class of strongly \\'{e}tale difference algebras, whose role in the study of difference equations is analogous to the role of \\'{e}tale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's decomposition theorem and we present applications to difference algebraic groups and the compatibility problem.

  15. Linear algebra done right

    CERN Document Server

    Axler, Sheldon

    2015-01-01

    This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the ...

  16. Particle-like structure of coaxial Lie algebras

    Science.gov (United States)

    Vinogradov, A. M.

    2018-01-01

    This paper is a natural continuation of Vinogradov [J. Math. Phys. 58, 071703 (2017)] where we proved that any Lie algebra over an algebraically closed field or over R can be assembled in a number of steps from two elementary constituents, called dyons and triadons. Here we consider the problems of the construction and classification of those Lie algebras which can be assembled in one step from base dyons and triadons, called coaxial Lie algebras. The base dyons and triadons are Lie algebra structures that have only one non-trivial structure constant in a given basis, while coaxial Lie algebras are linear combinations of pairwise compatible base dyons and triadons. We describe the maximal families of pairwise compatible base dyons and triadons called clusters, and, as a consequence, we give a complete description of the coaxial Lie algebras. The remarkable fact is that dyons and triadons in clusters are self-organised in structural groups which are surrounded by casings and linked by connectives. We discuss generalisations and applications to the theory of deformations of Lie algebras.

  17. The Lie algebra of the N=2-string

    International Nuclear Information System (INIS)

    Kugel, K.

    2006-01-01

    The theory of generalized Kac-Moody algebras is a generalization of the theory of finite dimensional simple Lie algebras. The physical states of some compactified strings give realizations of generalized Kac-Moody algebras. For example the physical states of a bosonic string moving on a 26 dimensional torus form a generalized Kac-Moody algebra and the physical states of a N=1 string moving on a 10 dimensional torus form a generalized Kac-Moody superalgebra. A natural question is whether the physical states of the compactified N=2-string also realize such an algebra. In this thesis we construct the Lie algebra of the compactified N=2-string, study its properties and show that it is not a generalized Kac-Moody algebra. The Fock space of a N=2-string moving on a 4 dimensional torus can be described by a vertex algebra constructed from a rational lattice of signature (8,4). Here 6 coordinates with signature (4,2) come from the matter part and 6 coordinates with signature (4,2) come from the ghost part. The physical states are represented by the cohomology of the BRST-operator. The vertex algebra induces a product on the vector space of physical states that defines the structure of a Lie algebra on this space. This Lie algebra shares many properties with generalized Kac-Moody algebra but we will show that it is not a generalized Kac-Moody algebra. (orig.)

  18. The Lie algebra of the N=2-string

    Energy Technology Data Exchange (ETDEWEB)

    Kugel, K

    2006-07-01

    The theory of generalized Kac-Moody algebras is a generalization of the theory of finite dimensional simple Lie algebras. The physical states of some compactified strings give realizations of generalized Kac-Moody algebras. For example the physical states of a bosonic string moving on a 26 dimensional torus form a generalized Kac-Moody algebra and the physical states of a N=1 string moving on a 10 dimensional torus form a generalized Kac-Moody superalgebra. A natural question is whether the physical states of the compactified N=2-string also realize such an algebra. In this thesis we construct the Lie algebra of the compactified N=2-string, study its properties and show that it is not a generalized Kac-Moody algebra. The Fock space of a N=2-string moving on a 4 dimensional torus can be described by a vertex algebra constructed from a rational lattice of signature (8,4). Here 6 coordinates with signature (4,2) come from the matter part and 6 coordinates with signature (4,2) come from the ghost part. The physical states are represented by the cohomology of the BRST-operator. The vertex algebra induces a product on the vector space of physical states that defines the structure of a Lie algebra on this space. This Lie algebra shares many properties with generalized Kac-Moody algebra but we will show that it is not a generalized Kac-Moody algebra. (orig.)

  19. Krichever-Novikov type algebras theory and applications

    CERN Document Server

    Schlichenmaier, Martin

    2014-01-01

    Krichever and Novikov introduced certain classes of infinite dimensionalLie algebrasto extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus. The author of this book generalized and extended them toa more general setting needed by the applications. Examples of applications are Conformal Field Theory, Wess-Zumino-Novikov-Witten models, moduli space problems, integrable systems, Lax operator algebras, and deformation theory of Lie algebra. Furthermore they constitute an important class of infinite dimensional Lie algebras which due to their geometric origin are

  20. The Das-Popowicz Moyal momentum algebra

    International Nuclear Information System (INIS)

    Boulahoual, A.; Sedra, M.B.

    2002-08-01

    We introduce in this short note some aspects of the Moyal momentum algebra that we call the Das-Popowicz Mm algebra. Our interest on this algebra is motivated by the central role that it can play in the formulation of integrable models and in higher conformal spin theories. (author)