Simple Lie groups without the approximation property
Haagerup, Uffe; de Laat, Tim
2013-01-01
For a locally compact group G, let A(G) denote its Fourier algebra, and let M0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-∗ topology...
Fricke Lie algebras and the genus zero property in Moonshine
Carnahan, Scott
2017-10-01
We give a new, simpler proof that the canonical actions of finite groups on Fricke-type Monstrous Lie algebras yield genus zero functions in generalized Monstrous Moonshine, using a Borcherds–Kac–Moody Lie algebra decomposition due to Jurisich. We describe a compatibility condition, arising from the no-ghost theorem in bosonic string theory, that yields the genus zero property. We give evidence for and against the conjecture that such a compatibility for symmetries of the Monster Lie algebra gives a characterization of the Monster group.
On properties of low-lying spin-1 hadron resonances
Chizhov, M. V.
2017-03-01
Properties of low-lying spin-1 hadron resonances are described in the review. It is shown how the Nambu-Jona-Lasinio model can be extended in the chiral invariant way by new tensor interactions. New mass formulas are obtained, which are not based on unitary symmetry groups but involve particles from different multiplets even with opposite parity. They all are in good agreement with experimental data. Dynamic properties of spin-1 mesons confirmed by the calculations performed using the QCD sum rule technique and the lattice calculations are understood and explained.
Lie algebras with given properties of subalgebras and elements
Zusmanovich, Pasha
2011-01-01
Results about the following classes of finite-dimensional Lie algebras over a field of characteristic zero are presented: anisotropic (i.e., Lie algebras for which each adjoint operator is semisimple), regular (i.e., Lie algebras in which each nonzero element is regular in the sense of Bourbaki), minimal nonabelian (i.e., nonabelian Lie algebras all whose proper subalgebras are abelian), and algebras of depth 2 (i.e., Lie algebras all whose proper subalgebras are abelian or minimal nonabelian).
Statistical properties of high-lying chaotic eigenstates
Li, B; Li, Baowen; Robnik, Marko
1995-01-01
We study the statistical properties of the high-lying chaotic eigenstates (200,000 and above) which are deep in the semiclassical regime. The system we are analyzing is the billiard system inside the region defined by the quadratic (complex) conformal map of the unit disk as introduced by Robnik (1983). We are using Heller's method of plane wave decomposition of the numerical eigenfunctions, and perform extensive statistical analysis with the following conclusions: (1) The local average probability density is in excellent agreement with the microcanonical assumption and all statistical properties are also in excellent agreement with the Gaussian random model; \\qquad (2) The autocorrelation function is found to be strongly direction dependent and only after averaging over all directions agrees well with Berry's (1977) prediction; \\qquad (3) Although the scars of unstable classical periodic orbits (in such ergodic regime) are expected to exist, so far we have not found any (around 200,000th state) but a scar-li...
SPECTRAL PROPERTIES OF SECOND ORDER DIFFERENTIAL OPERATORS ON TWO-STEP NILPOTENT LIE GROUPS
Niu Pengcheng
2000-01-01
In this paper, spectral properties of certain left invariant differential operators on two-step nilpotent Lie groups are completely described by using the theory of unitary irreducible representations and the Plancherel formulae on nilpotent Lie groups.
Regularity properties of infinite-dimensional Lie groups, and semiregularity
Glockner, Helge
2012-01-01
Let G be a Lie group modelled on a locally convex space, with Lie algebra g, and k be a non-negative integer or infinity. We say that G is C^k-semiregular if each C^k-curve c in g admits a left evolution Evol(c) in G. If, moreover, the map taking c to evol(c):=Evol(c)(1) is smooth, then G is called C^k-regular. For G a C^k-semiregular Lie group and m an order of differentiability, we show that evol is C^m if and only if Evol is C^m. If evol is continuous at 0, then evol is continuous. If G is...
78 FR 43857 - Order Relating to Yaming Nina Qi Hanson
2013-07-22
... Province, People's Republic of China (``Qi Hanson''), of its intention to initiate an administrative... old university classmates in China provided her with $75,000 to purchase the autopilots from the... money to finance the entire purchase. In so doing, Qi Hanson committed one violation of section...
Decay properties of low-lying collective states in sup 1 sup 3 sup 2 Ba
Gade, A; Meise, H; Gelberg, A; Brentano, P V
2002-01-01
The decay properties of low-lying collective states in sup 1 sup 3 sup 2 Ba were studied by means of gamma spectroscopy following the beta-decay of the 2 sup - ground state (T sub 1 sub / sub 2 =4.8 h) and a 6 sup - isomer (T sub 1 sub / sub 2 =24.3 min) of sup 1 sup 3 sup 2 La. The lanthanum nuclei were produced at the Cologne FN TANDEM accelerator using the reaction sup 1 sup 2 sup 2 Sn( sup 1 sup 4 N, 4n) sup 1 sup 3 sup 2 La. The gamma gamma coincidences and singles spectra were measured with the OSIRIS-cube spectrometer. Beside ground and quasi-gamma band many other low-lying states were observed. The gamma gamma angular correlations were analyzed to assign spins to the excited states, and to determine the multipolarities of the depopulating the gamma transitions. We also confirmed the expected dominant E2 character of transitions in the quasi-gamma band and from the quasi-gamma to the ground band but with a certain deviation: the decay 6 sup + sub 2->6 sup + sub 1 shows an unexpected large M1 fraction. ...
Rahaveski nimega olümpia / Martin Hanson
Hanson, Martin, 1984-
2008-01-01
Pekingi olümpiamängud toovad Hiinasse 700 miljardi krooni suuruse tuludevoo. 20 miljardit krooni tulu peaks andma ainuüksi olümpiamängude autoritasude ja teleõiguste müük, olümpiakeskuste ehitus ning piletimüük. Vt. samas: Sümbolid raha eest. Kommenteerib Martin Hanson
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
Papi, Paolo; Advances in Lie Superalgebras
2014-01-01
The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.
Stanislava Stoyanova
2013-04-01
Full Text Available This paper presents the results from the Bulgarian adaptation of Lie Scale from M. Bond’s questionnaire measuring defense styles and defensemechanisms. 994 subjects between 15 and 56 years participated in the study. All items had an optimal difficulty, and good discriminativepower. The factor structure of the scale was confirmed. Its reliability as internal consistency and test-retest reliability is acceptable. The normswere defined for the whole sample, not differentiated by social categories, because there were not any significant differences on the scalescore between the social categories of people. There were some significant differences on some items in gender, age sub-groups, familystatus, and occupation. These differences were consistent with some other authors’ findings when using some other scales measuring socialdesirability.
Parcels and Land Ownership, Kent Hanson 701 577 4543, Published in 2007, Williams County Government.
NSGIC GIS Inventory (aka Ramona) — This Parcels and Land Ownership dataset as of 2007. It is described as 'Kent Hanson 701 577 4543'. The extent of these data is generally Williams County, ND. This...
Some properties of the intersections of maximal subalgebras in Lie color algebras%李Color代数极大子代数的基本性质
宋华; 王晨迪
2012-01-01
In this paper,we develop initially the theory on the intersections of maximal subalgebras for Lie color algebras,obtain their some properties and give some necessary and sufficient conditions for solvable Lie color algebras and nilpotent Lie color algebras,respectively.%主要把Frattini子代数的性质推广到李Color代数,得到了它们的若干性质,并利用其性质分别给出可解和幂零李Color代数的几个充分必要条件.
The Virtues of the SDS and Its Associated Typology: A Second Response to Prediger and Hanson
Holland, John L.
1976-01-01
The author reviews the evidence for the beneficial effects of the Self-Directed Search (SDS), indicates that Hanson and Prediger have misinterpreted the theory, that their evidence is misleading, and that other evidence indicates that males and females of the same type are similar. The virtues of raw scores are summarized. (Author)
Axial Anomaly for Eguchi-Hanson Metrics with Nonzero Total Mass
ZHANG Xiao; ZHANG Yao-Zhong
2005-01-01
We compute the Dirac indexes for the two spin structures K0 and K1 for Eguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish in general, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes for the spin structure K0, and no axial anomaly exists in this case.
Lie groups and Lie algebras for physicists
Das, Ashok
2015-01-01
The book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras.
Bosonization and Lie Group Structure
Ha, Yuan K
2015-01-01
We introduce a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the group parameters. Bosonization is an extraordinary way of expressing the equation of motion of a complex fermion field in terms of a real scalar boson in two dimensions. All the properties of the fermion field theory are known to be preserved under this remarkable transformation with substantial simplification and elucidation of the original theory, much like Lie groups can be studied by their Lie algebras.
Weak Lie symmetry and extended Lie algebra
Goenner, Hubert [Institute for Theoretical Physics, Friedrich-Hund-Platz 1, University of Goettingen, D-37077 Gottingen (Germany)
2013-04-15
The concept of weak Lie motion (weak Lie symmetry) is introduced. Applications given exhibit a reduction of the usual symmetry, e.g., in the case of the rotation group. In this context, a particular generalization of Lie algebras is found ('extended Lie algebras') which turns out to be an involutive distribution or a simple example for a tangent Lie algebroid. Riemannian and Lorentz metrics can be introduced on such an algebroid through an extended Cartan-Killing form. Transformation groups from non-relativistic mechanics and quantum mechanics lead to such tangent Lie algebroids and to Lorentz geometries constructed on them (1-dimensional gravitational fields).
Lie Subalgebras in a Certain Operator Lie Algebra with Involution
Shan Li SUN; Xue Feng MA
2011-01-01
We show in a certain Lie'-algebra,the connections between the Lie subalgebra G+:＝G+G*+[G,G*],generated by a Lie subalgebra G,and the properties of G.This allows us to investigate some useful information about the structure of such two Lie subalgebras.Some results on the relations between the two Lie subalgebras are obtained.As an application,we get the following conclusion:Let A (∪) B(X)be a space of self-adjoint operators and L:＝A ⊕ iA the corresponding complex Lie*-algebra.G+＝G+G*+[G,G*]and G are two LM-decomposable Lie subalgebras of,L with the decomposition G+＝R(G+)+S,G＝RG+SG,and RG (∪) R(C+).Then G+ is ideally finite iff RG+:＝RG+RG*+[RG,RG*]is a quasisolvable Lie subalgebra,SG+:＝SG+SG*+[SG,SG*]is an ideally finite semisimple Lie subalgebra,and [RG,SG]＝[RG*,SG]＝{0}.
白瑞蒲; 程宇; 李佳倩; 孟伟
2014-01-01
3-Lie algebras have close relationships with many important fields in mathemat-ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char-acteristic zero are provided.
Debey, Evelyne; De Houwer, Jan; Verschuere, Bruno
2014-09-01
Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a two-step process, where the first step entails activating the truth, based upon which a lie response can be formulated in a second step. To investigate this hypothesis, we tried to capture the covert truth activation in a reaction-time based deception paradigm. Together with each question, we presented either the truth or lie response as distractors. If lying depends on the covert activation of the truth, deceptive responses would thus be facilitated by truth distractors relative to lie distractors. Our results indeed revealed such a "covert congruency" effect, both in errors and reaction times (Experiment 1). Moreover, stimulating participants to use the distractor information by increasing the proportion of truth distractor trials enlarged the "covert congruency" effects, and as such confirmed that the effects operate at a covert response level (Experiment 2). Our findings lend support to the idea that lying relies on a first step of truth telling, and call for a shift in theoretical thinking that highlights both the functional and interfering properties of the truth activation in the lying process. Copyright © 2014 Elsevier B.V. All rights reserved.
Kulinaarne palverännak piki Telliskivi tänavat / Martin Hanson, Ines Haak
Hanson, Martin, 1984-
2013-01-01
Toidukriitik Martin Hanson ja sisearhitekt Ines Haak Tallinna Telliskivi tänavat palistavatest söögipaikadest: restoran Kolm Sibulat (sisearhitektuur: Aivar Mühlbach, omanikud, 2012-2013), bistroo Kukeke (Anni Arro, Riina Eerik, 2011-2012), kohvik Reval (Ville Lausmäe, Kadi Karmann, Peeter Klaas, 2013), restoran F-Hoone (Ville Jehe, Steve Heinlo, 2010), baar Pudel (Raul Tiitus, Tarmo Piirmets, 2012-2013)
Solvable quadratic Lie algebras
ZHU; Linsheng
2006-01-01
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.
Infinite-dimensional Hamiltonian Lie superalgebras
无
2010-01-01
The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements.We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.
SOME RESULTS OF MODULAR LIE SUPERALGEBRAS
无
2006-01-01
In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups.Moreover, they announce and prove some results of modular complete Lie superalgebras.
Holomorph of Lie color algebras%Lie color代数的全形
杨恒云
2007-01-01
给出Lie color代数全形的一些性质,证明Lie color代数L的全形有分解(H)(L)=L(+)Z(H)(L)(L)的充分必要条件是它是完备Lie color代数.%To the holomorph of Lie color algebras, some properties are studied. A Lie color algebra L is complete if and only if (H)(L) = L(+)Z(H)(L) (L).
Stochastic Lie group integrators
Malham, Simon J A
2007-01-01
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie algebra via the exponential map. We construct an approximation to the stochastic flow in the Lie algebra via closed operations and then push back to the Lie group and then to the manifold, thus ensuring our approximation lies in the manifold. We call such schemes stochastic Munthe-Kaas methods after their deterministic counterparts. We also present stochastic Lie group integration schemes based on Castell--Gaines methods. These involve using an underlying ordinary differential integrator to approximate the flow generated by a truncated stochastic exponential Lie series. They become stochastic Lie group integrator schemes if...
DERIVATIONS AND EXTENSIONS OF LIE COLOR ALGEBRA
Zhang Qingcheng; Zhang Yongzheng
2008-01-01
In this article, the authors obtain some results concerning derivations of fi-nitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L) and central extension H2(L, F) on some Lie color algebras. Meanwhile, they generalize the notion of double extension to quadratic Lie color algebras, a sufficient con-dition for a quadratic Lie color algebra to be a double extension and further properties are given.
2008-01-01
The calculations on the potential energy curves and spectroscopic constants of the ground and low-lying excited states of BrCl+,one of the important molecular ions in environment science,have been performed by using the multireference configuration interaction method at high level of theory in quantum chemistry.Through analyses of the effects of the spin-orbit coupling interaction on the elec-tronic structures and spectroscopic properties,the multiconfiguration characteristic of the X2Π ground state and low-lying excited states was established.The spin-orbit coupling splitting energy of the X2 Π ground state was calculated to be 1814 cm-1,close to the experimental value 2070 cm-1.The spin-orbit coupling splitting energy of the 2Π(Ⅱ) exited state was predicted to be 766 cm-1.The transition dipole moments and Frank-Condon factors of the 3/2(Ⅲ)-X3/2 and 1/2(Ⅲ)-1/2(I) transitions were estimated,and the radiative lifetimes of the two transitions were briefly discussed.
WANG MingWei; WANG BingWu; CHEN ZhiDa
2008-01-01
The calculations on the potential energy curves and spectroscopic constants of the ground and low-lying excited states of BrCl+, one of the important molecular ions in environment science, have been performed by using the multireference configuration interaction method at high level of theory in quantum chemistry. Through analyses of the effects of the spin-orbit coupling interaction on the electronic structures and spectroscopic properties, the multiconfiguration characteristic of the X2∏ ground state and low-lying excited states was established. The spin-orbit coupling splitting energy of the X2∏ ground state was calculated to be 1814 cm-1, close to the experimental value 2070 cm-1. The spin-orbit coupling splitting energy of the 2∏(Ⅱ) exited state was predicted to be 766 cm-1. The transition dipole moments and Frank-Condon factors of the 3/2(Ⅲ)-X3/2 and 1/2(Ⅲ)-1/2(Ⅰ) transitions were estimated, and the radiative lifetimes of the two transitions were briefly discussed.
Monmonier, Mark
2005-01-01
Darrell Huff’s How to Lie with Statistics was the inspiration for How to Lie with Maps, in which the author showed that geometric distortion and graphic generalization of data are unavoidable elements of cartographic representation. New examples of how ill-conceived or deliberately contrived statistical maps can greatly distort geographic reality demonstrate that lying with maps is a special case of lying with statistics. Issues addressed include the effects of map scale on geometry and featu...
Heyman, Gail D.; Luu, Diem H.; Lee, Kang
2009-01-01
The present set of studies identifies the phenomenon of "parenting by lying", in which parents lie to their children as a means of influencing their emotional states and behaviour. In Study 1, undergraduates (n = 127) reported that their parents had lied to them while maintaining a concurrent emphasis on the importance of honesty. In Study 2 (n =…
Zaitsev, N. L.; Nechaev, I. A.; Höfer, U.; Chulkov, E. V.
2016-10-01
The geometrical and electronic properties of the monolayer (ML) of tetracene (Tc) molecules on Ag(111) are systematically investigated by means of DFT calculations with the use of a localized basis set. The bridge and hollow adsorption positions of the molecule in the commensurate γ -Tc/Ag(111) are revealed to be the most stable and equally favorable irrespective to the approximation chosen for the exchange-correlation functional. The binding energy is entirely determined by the long-range dispersive interaction. The former lowest unoccupied molecular orbital remains being unoccupied in the case of γ -Tc/Ag(111) as well as in the α phase with increased coverage. The unit cell of the α phase with point-on-line registry was adapted for calculations based on the available experimental data and computed structures of the γ phase. The calculated position of the Tc/Ag(111) interface state is found to be noticeably dependent on the lattice constant of the substrate, however its energy shift with respect to the Shockley surface state of the unperturbed clean side of the slab is sensitive only to the adsorption distance and in good agreement with the experimentally measured energy shift.
Engel Subalgebras of n-Lie Algebras
Donald W. BARNES
2008-01-01
Engel subalgebras of finite-dimensional n Lie algebras are shown to have similar properties to those of Lie algebras.Using these,it is shown that an n Lie algebra,all of whose maximal subalgebras are ideals,is nilpotent.A primitive 2-soluble n Lie algebra is shown to split over its minimal ideal, and all the complements to its minimal ideal are conjugate.A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel,provided that the field has su .ciently many elements. Cartan subalgebras are shown to have a property analogous to intravariance.
Finite dimensional quadratic Lie superalgebras
Jarvis, Peter; Yates, Luke
2010-01-01
We consider a special class of Z_2-graded, polynomial algebras of degree 2, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. Based on the factorisation of the enveloping algebra, we derive the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate the method for one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.
Additive Lie ($\\xi$-Lie) Derivations and Generalized Lie ($\\xi$-Lie) Derivations on Prime Algebras
Qi, Xiaofei
2010-01-01
The additive (generalized) $\\xi$-Lie derivations on prime algebras are characterized. It is shown, under some suitable assumption, that an additive map $L$ is an additive (generalized) Lie derivation if and only if it is the sum of an additive (generalized) derivation and an additive map from the algebra into its center vanishing all commutators; is an additive (generalized) $\\xi$-Lie derivation with $\\xi\
Generalized derivations of Lie triple systems
Zhou Jia
2016-01-01
Full Text Available In this paper, we present some basic properties concerning the derivation algebra Der (T, the quasiderivation algebra QDer (T and the generalized derivation algebra GDer (T of a Lie triple system T, with the relationship Der (T ⊆ QDer (T ⊆ GDer (T ⊆ End (T. Furthermore, we completely determine those Lie triple systems T with condition QDer (T = End (T. We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.
Verschuere, B.; Spruyt, A.; Meijer, E.H.; Otgaar, H.
2011-01-01
Brain imaging studies suggest that truth telling constitutes the default of the human brain and that lying involves intentional suppression of the predominant truth response. By manipulating the truth proportion in the Sheffield lie test, we investigated whether the dominance of the truth response i
Verschuere, B.; Spruyt, A.; Meijer, E.H.; Otgaar, H.
2011-01-01
Brain imaging studies suggest that truth telling constitutes the default of the human brain and that lying involves intentional suppression of the predominant truth response. By manipulating the truth proportion in the Sheffield lie test, we investigated whether the dominance of the truth response
Vermillion, Marti
1985-01-01
Lying is a symptom of a much broader problem. Primary motivations are need for acceptance, fear of punishment, and desire for attention. Children learn about honesty through observation, both directly and indirectly. Admitting mistakes, especially to children, is invaluable and can help break the lying syndrome. (MT)
Post-Lie algebras and factorization theorems
Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans
2017-09-01
In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.
Medicine, lies and deceptions.
Benn, P
2001-04-01
This article offers a qualified defence of the view that there is a moral difference between telling lies to one's patients, and deceiving them without lying. However, I take issue with certain arguments offered by Jennifer Jackson in support of the same conclusion. In particular, I challenge her claim that to deny that there is such a moral difference makes sense only within a utilitarian framework, and I cast doubt on the aptness of some of her examples of non-lying deception. But I argue that lies have a greater tendency to damage trust than does non-lying deception, and suggest that since many doctors do believe there is a moral boundary between the two types of deception, encouraging them to violate that boundary may have adverse general effects on their moral sensibilities.
Evasive Lying in Strategic Communication
Khalmetski, Kiryl; Rockenbach, Bettina; Werner, Peter
2017-01-01
In a sender-receiver game we investigate if sanctions for lying induce more truth-telling. Senders may not only choose between truth-telling and (explicit) lying, but may also engage in evasive lying by credibly pretending not to know. Sanctions promote truth-telling if senders cannot engage in evasive lying. If evasive lying is possible, explicit lying is largely substituted by evasive lying, in line with the notion that evasive lying is perceived as sufficiently less psychologically costly.
Induced Modules of Restricted Lie Superalgebras
刘文德
2005-01-01
In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established.Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
Bakhurst, D
1992-06-01
This article challenges Jennifer Jackson's recent defence of doctors' rights to deceive patients. Jackson maintains there is a general moral difference between lying and intentional deception: while doctors have a prima facie duty not to lie, there is no such obligation to avoid deception. This paper argues 1) that an examination of cases shows that lying and deception are often morally equivalent, and 2) that Jackson's position is premised on a species of moral functionalism that misconstrues the nature of moral obligation. Against Jackson, it is argued that both lying and intentional deception are wrong where they infringe a patient's right to autonomy or his/her right to be treated with dignity. These rights represent 'deontological constraints' on action, defining what we must not do whatever the functional value of the consequences. Medical ethics must recognise such constraints if it is to contribute to the moral integrity of medical practice.
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...
Additive Lie (ζ-Lie) Derivations and Generalized Lie (ζ-Lie)Derivations on Prime Algebras
Xiao Fei QI; Jin Chuan HOU
2013-01-01
The additive (generalized) ζ-Lie derivations on prime algebras are characterized.It is shown,under some suitable assumptions,that an additive map L is an additive generalized Lie derivation if and only if it is the sum of an additive generalized derivation and an additive map from the algebra into its center vanishing all commutators; is an additive (generalized) ζ-Lie derivation with ζ ≠ 1 if and only if it is an additive (generalized) derivation satisfying L(ζA) =ζL(A) for all A.These results are then used to characterize additive (generalized) ζ-Lie derivations on several operator algebras such as Banach space standard operator algebras and von Neumman algebras.
Lying, honor, and contradiction
Michael Gilsenan
2016-01-01
.... +Superscript 1 -Superscript With a particular concentration on the manifold practices of what will be called "lying," I shall try to show the way in which individuals in a Lebanese village negotiate...
ON THE PRIMARY DECOMPOSITION THEOREM OF MODULAR LIE SUPERALGEBRAS
CHEN LIANGYUN; MENG DAOJI
2005-01-01
This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primry decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras (see [5, 6]). Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.
Abstract Lie groups and locally compact topological groups
Jacek Lech
2004-05-01
Full Text Available We introduce a notion of abstract Lie group by means of the mapping which plays the role of the evolution operator. We show some basic properties of such groups very similar to the fundamentals of the infinite dimensional Lie theory. Next we give remarkable examples of abstract Lie groups which are not necessarily usual Lie groups. In particular, by making use of Yamabe theorem we prove that any locally compact topological group admits the structure of abstract Lie group and that the Lie algebra and the exponential mapping of it coincide with those determined by the Lie group structure.
Classification and identification of Lie algebras
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...
Seron, X
2014-10-01
The issue of lying occurs in neuropsychology especially when examinations are conducted in a forensic context. When a subject intentionally either presents non-existent deficits or exaggerates their severity to obtain financial or material compensation, this behaviour is termed malingering. Malingering is discussed in the general framework of lying in psychology, and the different procedures used by neuropsychologists to evidence a lack of collaboration at examination are briefly presented and discussed. When a lack of collaboration is observed, specific emphasis is placed on the difficulty in unambiguously establishing that this results from the patient's voluntary decision.
Xing, Wei; Shi, Deheng; Sun, Jinfeng; Zhu, Zunlue
2017-10-01
This paper studied the spectroscopic and transition properties of 36 low-lying states, which came from the first two dissociation limits of B2 molecule. The potential energy curves were calculated with the complete active space self-consistent field (CASSCF) method, which was followed by the internally contracted multireference configuration interaction (icMRCI) plus Davidson modification (icMRCI + Q) approach. Of these 36 states, the 25Σu-, 15Σu+, 25Πu, and 15Δu states were repulsive; the B3Δu, E3Σu+, f1Σu-, g1Πg, 23Πu, 33Σg-, 33Πu, 15Πg, and 33Σu+ states had double wells; the B3Δu, E3Σu+, G3Σu+, f1Σu-, g1Πg, 33Σg-, 23Πu, 33Πu, 15Πg, 25Πg, 25Σg-, and 33Σu+ states had one barrier; the 25Σg- state and the second wells of B3Δu, E3Σu+, 15Πg, f1Σu-, g1Πg, and 23Πu states were weakly bound; and the 25Σg- state had no vibrational levels. The avoided crossings existed between the B3Δu and 23Δu states, the E3Σu+ and G3Σu+ states, the G3Σu+ and 33Σu+ states, the 33Σu+ and 43Σu+ states, the 23Πu and 33Πu states, the g1Πg and 21Πg states, the 23Σg- and 33Σg- states, the 15Πg and 25Πg states, the 25Πg and 35Πg states, the 25Σg- and 35Σg- states, as well as the F3Πg and 33Πg states. Core-valence correlation and scalar relativistic corrections were taken into account. The extrapolation to the complete basis set limit was done. The spectroscopic parameters and vibrational properties were obtained. The transition dipole moments were calculated. Franck-Condon factors of some transitions were evaluated. The spin-orbit coupling (SOC) effect on the spectroscopic parameters and vibrational properties is tiny and sometimes even can be negligible. The results determined in this paper can provide some powerful guidelines to observe these states, in particular the states which have not been studied in the experiment.
Mass transfer coefficients in a hanson mixer-settler extraction column
M. Torab-Mostaedi
2008-09-01
Full Text Available The volumetric overall mass transfer coefficients in a pilot plant Hanson mixer-settler extraction column of seven stages have been measured using toluene-acetone-water system. The effects of agitation speed and dispersed and continuous phases flow rates on volumetric overall mass transfer coefficients have been investigated. The results show that the volumetric overall mass transfer coefficient increases with increase in agitation speed and reaches a maximum. After having reached its maximum, it falls with further increase in agitation speed. It was found that the volumetric overall mass transfer coefficient increases with increase in dispersed phase flow rate, while it decreases with increase in continuous phase flow rate. By using interfacial area, the overall mass transfer coefficients for continuous and dispersed phases are determined from volumetric coefficients. An empirical correlation for prediction of the continuous phase overall mass transfer coefficient is proposed in terms of Sherwood and Reynolds numbers. Also the experimental data of the column investigated are compared with data for various extraction columns. Comparison between theoretical models and experimental results for the dispersed phase mass transfer coefficient shows that these models do not have enough accuracy for column design. Using effective diffusivity in the Gröber equation results in more accurate prediction of overall mass transfer coefficient. The prediction of overall mass transfer coefficients from the presented equations is in good agreement with experimental results.
H. van Ditmarsch (Hans); D.J.N. van Eijck (Jan); F.A.G. Sietsma (Floor); Y. Wang (Yanjing); D.J.N. van Eijck (Jan); R. Verbrugge
2011-01-01
htmlabstractWe look at lying as an act of communication, where (i) the proposition that is communicated is not true, (ii) the utterer of the lie knows (or believes) that what she communicates is not true, and (iii) the utterer of the lie intends the lie to be taken as truth. Rather than dwell on
Forte, G; March, N H; Pucci, R
2013-01-01
After some introductory comments relating to antiferromagnetism of crystalline O_2, and brief remarks on the geometry of ozone, Hartree-Fock (HF) theory plus second-order Moller-Plesset (MP2) corrections are used to predict the nuclear structure of low-lying isomers of free-space O_n clusters, for n=6, 8, and 12. The equilibrium nuclear-nuclear potential energy is also discussed in relation to the number n of oxygen atoms in the cluster.
Lie algebraic noncommutative gravity
Banerjee, Rabin; Mukherjee, Pradip; Samanta, Saurav
2007-06-01
We exploit the Seiberg-Witten map technique to formulate the theory of gravity defined on a Lie algebraic noncommutative space-time. Detailed expressions of the Seiberg-Witten maps for the gauge parameters, gauge potentials, and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.
Introduction to quantum Lie algebras
Delius, G W
1996-01-01
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras \\uqg. The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. In this paper the recent general results about quantum Lie algebras are introduced with the help of the explicit example of (sl_2)_h.
Lie groups, lie algebras, and representations an elementary introduction
Hall, Brian
2015-01-01
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compac...
Forte, G. [Dipartimento di Scienze del Farmaco, Università di Catania, Viale A. Doria, 6, I-95126 Catania (Italy); Angilella, G.G.N., E-mail: giuseppe.angilella@ct.infn.it [Dipartimento di Fisica e Astronomia, Università di Catania, Via S. Sofia, 64, I-95123 Catania (Italy); Scuola Superiore di Catania, Università di Catania, Via Valdisavoia, 9, I-95123 Catania (Italy); CNISM, UdR Catania, Via S. Sofia, 64, I-95123 Catania (Italy); INFN, Sez. Catania, Via S. Sofia, 64, I-95123 Catania (Italy); March, N.H. [Department of Physics, University of Antwerp, Groenenborgerlaan, 171, B-2020 Antwerp (Belgium); Oxford University, Oxford (United Kingdom); Pucci, R. [Dipartimento di Fisica e Astronomia, Università di Catania, Via S. Sofia, 64, I-95123 Catania (Italy); CNISM, UdR Catania, Via S. Sofia, 64, I-95123 Catania (Italy)
2013-04-01
After some introductory comments relating to antiferromagnetism of crystalline O{sub 2}, and brief remarks on the geometry of ozone, Hartree–Fock (HF) theory plus second-order Møller–Plesset (MP2) corrections are used to predict the nuclear structure of low-lying isomers of free-space O{sub n} clusters, for n=6,8, and 12. The equilibrium nuclear–nuclear potential energy is also discussed in relation to the number n of oxygen atoms in the cluster.
Lie algebraic Noncommutative Gravity
Banerjee, R; Samanta, S; Banerjee, Rabin; Mukherjee, Pradip; Samanta, Saurav
2007-01-01
The minimal (unimodular) formulation of noncommutative general relativity, based on gauging the Poincare group, is extended to a general Lie algebra valued noncommutative structure. We exploit the Seiberg -- Witten map technique to formulate the theory as a perturbative Lagrangian theory. Detailed expressions of the Seiberg -- Witten maps for the gauge parameters, gauge potentials and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.
NONE
1996-02-01
The Department of Energy has prepared an Environmental Assessment (DOE/EA-1143) evaluating the construction, equipping and operation of the proposed Lied Transplant Center at the University of Nebraska Medical Center in Omaha, Nebraska. Based on the analysis in the EA, the DOE has determined that the proposed action does not constitute a major federal action significantly affecting the quality of the human environment within the meaning of the National Environmental Policy Act of 1969 (NEPA). Therefore, the preparation of an Environmental Statement in not required.
Police lie detection accuracy: the effect of lie scenario.
O'Sullivan, Maureen; Frank, Mark G; Hurley, Carolyn M; Tiwana, Jaspreet
2009-12-01
Although most people are not better than chance in detecting deception, some groups of police professionals have demonstrated significant lie detection accuracy. One reason for this difference may be that the types of lies police are asked to judge in scientific experiments often do not represent the types of lies they see in their profession. Across 23 studies, involving 31 different police groups in eight countries, police officers tested with lie detection scenarios using high stakes lies (i.e., the lie was personally involving and/or resulted in substantial rewards or punishments for the liar) were significantly more accurate than law enforcement officials tested with low stakes lies. Face validity and construct validity of various lie scenarios are differentiated.
[Diagnostic imaging of lying].
Lass, Piotr; Sławek, Jarosław; Sitek, Emilia; Szurowska, Edyta; Zimmermann, Agnieszka
2013-01-01
Functional diagnostic imaging has been applied in neuropsychology for more than two decades. Nowadays, the functional magnetic resonance (fMRI) seems to be the most important technique. Brain imaging in lying has been performed and discussed since 2001. There are postulates to use fMRI for forensic purposes, as well as commercially, e.g. testing the loyalty of employees, especially because of the limitations of traditional polygraph in some cases. In USA fMRI is performed in truthfulness/lying assessment by at least two commercial companies. Those applications are a matter of heated debate of practitioners, lawyers and specialists of ethics. The opponents of fMRI use for forensic purposes indicate the lack of common agreement on it and the lack of wide recognition and insufficient standardisation. Therefore it cannot serve as a forensic proof, yet. However, considering the development of MRI and a high failure rate of traditional polygraphy, forensic applications of MRI seem to be highly probable in future.
Telling Lies: The Irrepressible Truth?
Williams, Emma J.; Bott, Lewis A.; Patrick, John; Lewis, Michael B.
2013-01-01
Telling a lie takes longer than telling the truth but precisely why remains uncertain. We investigated two processes suggested to increase response times, namely the decision to lie and the construction of a lie response. In Experiments 1 and 2, participants were directed or chose whether to lie or tell the truth. A colored square was presented and participants had to name either the true color of the square or lie about it by claiming it was a different color. In both experiments we found that there was a greater difference between lying and telling the truth when participants were directed to lie compared to when they chose to lie. In Experiments 3 and 4, we compared response times when participants had only one possible lie option to a choice of two or three possible options. There was a greater lying latency effect when questions involved more than one possible lie response. Experiment 5 examined response choice mechanisms through the manipulation of lie plausibility. Overall, results demonstrate several distinct mechanisms that contribute to additional processing requirements when individuals tell a lie. PMID:23573277
Group discussion improves lie detection
Nadav Klein; Nicholas Epley
2015-01-01
... identify when a person is lying. These experiments demonstrate that the group advantage in lie detection comes through the process of group discussion, and is not a product of aggregating individual opinions...
Lying because we care: Compassion increases prosocial lying.
Lupoli, Matthew J; Jampol, Lily; Oveis, Christopher
2017-07-01
Prosocial lies, or lies intended to benefit others, are ubiquitous behaviors that have important social and economic consequences. Though emotions play a central role in many forms of prosocial behavior, no work has investigated how emotions influence behavior when one has the opportunity to tell a prosocial lie-a situation that presents a conflict between two prosocial ethics: lying to prevent harm to another, and honesty, which might also provide benefits to the target of the lie. Here, we examine whether the emotion of compassion influences prosocial lying, and find that compassion causally increases and positively predicts prosocial lying. In Studies 1 and 2, participants evaluated a poorly written essay and provided feedback to the essay writer. Experimentally induced compassion felt toward the essay writer (Study 1) and individual differences in trait compassion (Study 2) were positively associated with inflated feedback to the essay writer. In both of these studies, the relationship between compassion and prosocial lying was partially mediated by an enhanced importance placed on preventing emotional harm. In Study 3, we found moderation such that experimentally induced compassion increased lies that resulted in financial gains for a charity, but not lies that produced financial gains for the self. This research illuminates the emotional underpinnings of the common yet morally complex behavior of prosocial lying, and builds on work highlighting the potentially harmful effects of compassion-an emotion typically seen as socially beneficial. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
H. van Ditmarsch (Hans); D.J.N. van Eijck (Jan); F.A.G. Sietsma (Floor)
2012-01-01
textabstractWe model lying as a communicative act changing the beliefs of the agents in a multi-agent system. With Augustine, we see lying as an utterance believed to be false by the speaker and uttered with the intent to deceive the addressee. The deceit is successful if the lie is believed
Debey, E.; De Houwer, J.; Verschuere, B.
2014-01-01
Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a
Debey, E.; De Houwer, J.; Verschuere, B.
2014-01-01
Cognitive models of deception focus on the conflict-inducing nature of the truth activation during lying. Here we tested the counterintuitive hypothesis that the truth can also serve a functional role in the act of lying. More specifically, we examined whether the construction of a lie can involve a
Dotsenko, V.; Shadrin, S.; Vallette, B.
2016-01-01
In this paper, we develop the deformation theory controlled by pre-Lie algebras; the main tool is a new integration theory for preLie algebras. The main field of application lies in homotopy algebra structures over a Koszul operad; in this case, we provide a homotopical description of the associated
Restricted and quasi-toral restricted Lie-Rinehart algebras
Sun Bing
2015-09-01
Full Text Available In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension should be.
Quantization on nilpotent Lie groups
Fischer, Veronique
2016-01-01
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.
Lie algebras and linear differential equations.
Brockett, R. W.; Rahimi, A.
1972-01-01
Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.
A low-lying long-lived (26±1 ms) isomer in $^{34}$Al has been observed recently and assigned as 1$^{+}$ state of intruder character. It was populated in $^{36}$S fragmentation and feeds, in $\\beta$-decay, the 0$_{2}^{+}$ state in $^{34}$Si whose excitation energy and lifetime were determined in an electron-positron pairs spectroscopy experiment. In the present experiment we intend to measure for the first time the $\\gamma$-rays following the $\\beta$-decay of $^{34}$Mg. Despite the interest for $^{34}$Mg, the up-right corner of the “N$\\thicksim$20 island of inversion”, the only information on its $\\beta$-decay is the lifetime of 20±10 ms, determined from $\\beta$-neutron coincidences. As a result of the proposed experiment, we expect to place the first transitions in the level scheme of $^{34}$Al and to strongly populate the newly observed isomer, measuring its excitation energy, if the branching ratio to 4$^{−}$ ground state is significant. Theoretical estimations for the $\\beta$-decay of the new isome...
Integrability of Lie Systems Through Riccati Equations
Cariñena, José F.; de Lucas, Javier
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.
Integrability of Lie systems through Riccati equations
Cariñena, José F
2010-01-01
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides us with a unified geometrical viewpoint that allows us to analyse some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalised to describe integrability conditions for any Lie system. Finally, we show the usefulness of our treatment in order to study the problem of the linearisability of Riccati equations.
Anjan Chattopadhyay
2012-09-01
Semiempirical and ab initio-based CI methods have been employed to study the low-lying electronic states of 2,4-pentadien-1-iminium cation and its N-substituted analogues with electron-donating (methyl, isopropyl) and electron-withdrawing (fluoromethyl) groups on nitrogen. Variations of the dihedral angles (Γ3, Γ4) of the ground state have given the global minima and global maxima at (180°, 180°) and (90°, 0°) conformations, respectively, with some exceptions in the case of fluoromethyl compound. Increase in the +I effect on nitrogen shifts the TICT conical intersection point away from the 90° (Γ3 dihedral angle) value, when the Γ4 value is kept fixed at 180°. Transition moment values of the allowed S0(1A -like) → S1 (2B-like) transitions are expectedly higher than the forbidden S0(1A -like) → S2(2A -like) transitions by almost 5.6 D. Radiative lifetime values of the first excited states are calculated to be around 215 ps for all the four compounds. At (180°, 180°) conformation the vertical excitation energy (VEE) between the S0 and S1 states of the 2,4-pentadieniminium cation is found to be 3.3 eV, which corresponds to the absorption wavelength value of roughly 375 nm. The VEE value increases with substituents having +I effect on nitrogen, while for the fluoromethyl compound it is calculated to be around 2.85 eV. The energy gap between the first two excited singlet states is found to have the least value in the isopropyl-substituted compound, where the S2 state contains a huge contribution from the HOMO2→LUMO2 configuration.
Lie groups and automorphic forms
Ji, Lizhen; Xu, H W; Yau, Shing-Tung
2006-01-01
Lie groups are fundamental objects in mathematics. They occur naturally in differential geometry, algebraic geometry, representation theory, number theory, and other areas. Closely related are arithmetic subgroups, locally symmetric spaces and the spectral theory of automorphic forms. This book consists of five chapters which give comprehensive introductions to Lie groups, Lie algebras, arithmetic groups and reduction theories, cohomology of arithmetic groups, and the Petersson and Kuznetsov trace formulas.
Differential geometry on Lie groups
2013-01-01
Resumo: Neste trabalho estudamos os aspectos geométricos dos grupos de Lie do ponto de vista da geometria Riemanniana, geometria Hermitiana e geometria Kähler, através das estruturas geométricas invariantes associadas. Exploramos resultados relacionados às curvaturas da variedade Riemanniana subjacente a um grupo de Lie através do estudo de sua álgebra de Lie correspondente. No contexto da geometria Hermitiana e geometria Kähler, para um caso concreto de grupo de Lie complexo, investigaram su...
Affective Priming Caused by Lying
Megumi Sato
2011-10-01
Full Text Available Typically, arousal increases when telling a lie, as indicated in psychophysiological studies about lie detection. But the emotional valence induced by lying is unknown, though intuition indicates that it may be negative. Indeed, the Electrodermal Activity (EDA, used in such studies, only shows arousal changes during an emotional response. In this study, we examined the emotional valence induced by lying using two tasks. First, in the deceptive task, participants answered “no” to every question regarding the nature of displayed playing cards. Therefore, they told a lie about specific cards. During the task, their EDA was recorded. Secondly, in the figure estimation task, they assessed pictures by “like” or “dislike” after looking at playing cards visibly or subliminally as prime stimuli. We expected them to tend to estimate figures by “dislike” when cards relevant to deception were previously shown. This would mean that an affective priming effect due to telling a lie happened. Actually, this effect was found only when prime stimuli were displayed visibly. This result suggests that lying per se induces negative emotions even without motivation or punishment due to lying. Furthermore, we found that such effect was more blatant in participants whose EDA changes were salient while lying.
Sectional and Ricci Curvature for Three-Dimensional Lie Groups
Gerard Thompson
2016-01-01
Full Text Available Formulas for the Riemann and Ricci curvature tensors of an invariant metric on a Lie group are determined. The results are applied to a systematic study of the curvature properties of invariant metrics on three-dimensional Lie groups. In each case the metric is reduced by using the automorphism group of the associated Lie algebra. In particular, the maximum and minimum values of the sectional curvature function are determined.
Theatres of the lie: 'crazy' deception and lying as drama.
Dongen, Els van
2002-08-01
In this article, the author argues that lying is drama, theatre, which brings about transition, reflection, reversal and involvement of the participants in the drama. By means of ethnographic data of a psychiatric ward, the author shows that lying of mental patients is not pathological, but a ritual of affliction. By using Turner's theory about rituals and performance and Goffman's theory about presentation of the self it will be showed that lying serves the redefinition of reciprocity and solidarity. With the help of Bakhtin's work on Rabelais, the author discusses the nature of the drama of the lie. It is concluded that a perspective on lying as theatre may be of use outside psychiatric wards and will occur in imbalanced power relationships.
Deciding isomorphism of Lie algebras
Graaf, W.A. de
2001-01-01
When doing calculations with Lie algebras one of the main problems is to decide whether two given Lie algebras are isomorphic. A partial solution to this problem is obtained by calculating structural invariants. There is also a direct method available which involves the computation of Grobner bases.
The low lying glueball spectrum
Adam Szczepaniak; Eric Swanson
2003-12-18
The complete low-lying positive charge conjugation glueball spectrum is obtained from QCD. The formalism relies on the construction of an efficient quasiparticle gluon basis for Hamiltonian QCD in Coulomb gauge. The resulting rapidly convergent Fock space expansion is exploited to derive quenched low-lying glueball masses with no free parameters which are in remarkable agreement with lattice gauge theory.
Lie Symmetries of Ishimori Equation
SONG Xu-Xia
2013-01-01
The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.
关于河北平原区深层地下水资源属性的探讨%Discussions on the property of deep-lying groundwater resources in Hebei Plain
王欣宝; 张树刚; 谷明旭; 李玉龙
2012-01-01
以河北平原为例,采用同位素、地下水资源评价和地下水水位动态3种思路分析了深层地下水资源属性。根据实测地面沉降量反求深层地下水储存资源量的构成,确定了在以往的深层地下水资源计算时储存资源量少计算了32.77%,弹性释放系数比以往的数据大;根据深层地下水动态特征,分析认为深层地下水资源在同一水文年内可以得到部分恢复,在深层地下水降落漏斗区地下水循环速率将加大,并根据沉积学的观点,认为河北平原含水层在各期古河道带交叉重叠部位或在重叠部位附近可能是连通的,浅层地下水可以沿着各期古河道带沉积的砂性土构成的含水层向下补给深层地下水,其补给量远大于通过巨厚的黏性土层向深层地下水的越流补给。%Taking Hebei Plain as an example,the authors adopt isotope geology,groundwater resources evaluation and groundwater level dynamic method to analyze the property of deep-lying groundwater resources.The constitution of deep-lying groundwater exploitation is derived on the basis of the measured land subsidence data.It is determined that the previously calculated storage resource is 32.77% underestimated,and the data of elastic release coefficient at present is larger than the original data.According to the dynamic characteristics of deep-lying groundwater,it is proposed that the deep groundwater resources in the same hydrological year can be partially restored.In deep-lying groundwater funnel area,the groundwater circulation rate will increase,and according to the view point of sedimentology,the aquifer of the overlapping part of the ancient river and its vicinity is probably run-through.Shallow groundwater could pass downward along the aquifer of the ancient river sedimentary sand beds to recharge the deep-lying groundwater,and the amount of supply may be much greater than those recharges passing through the thick clay layer to the deep-lying
Lying despite telling the truth.
Wiegmann, Alex; Samland, Jana; Waldmann, Michael R
2016-05-01
According to the standard definition of lying an utterance counts as a lie if the agent believes the statement to be false. Thus, according to this view it is possible that a lie states something that happens to be true. This subjective view on lying has recently been challenged by Turri and Turri (2015) who presented empirical evidence suggesting that people only consider statements as lies that are objectively false (objective view). We argue that the presented evidence is in fact consistent with the standard subjective view if conversational pragmatics is taken into account. Three experiments are presented that directly test and support the subjective view. An additional experiment backs up our pragmatic hypothesis by using the uncontroversial case of making a promise.
Group discussion improves lie detection.
Klein, Nadav; Epley, Nicholas
2015-06-16
Groups of individuals can sometimes make more accurate judgments than the average individual could make alone. We tested whether this group advantage extends to lie detection, an exceptionally challenging judgment with accuracy rates rarely exceeding chance. In four experiments, we find that groups are consistently more accurate than individuals in distinguishing truths from lies, an effect that comes primarily from an increased ability to correctly identify when a person is lying. These experiments demonstrate that the group advantage in lie detection comes through the process of group discussion, and is not a product of aggregating individual opinions (a "wisdom-of-crowds" effect) or of altering response biases (such as reducing the "truth bias"). Interventions to improve lie detection typically focus on improving individual judgment, a costly and generally ineffective endeavor. Our findings suggest a cheap and simple synergistic approach of enabling group discussion before rendering a judgment.
Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
Yvette Kosmann-Schwarzbach
2008-01-01
Full Text Available After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper.
Detecting true lies: police officers' ability to detect suspects' lies.
Mann, Samantha; Vrij, Aldert; Bull, Ray
2004-02-01
Ninety-nine police officers, not identified in previous research as belonging to groups that are superior in lie detection, attempted to detect truths and lies told by suspects during their videotaped police interviews. Accuracy rates were higher than those typically found in deception research and reached levels similar to those obtained by specialized lie detectors in previous research. Accuracy was positively correlated with perceived experience in interviewing suspects and with mentioning cues to detecting deceit that relate to a suspect's story. Accuracy was negatively correlated with popular stereotypical cues such as gaze aversion and fidgeting. As in previous research, accuracy and confidence were not significantly correlated, but the level of confidence was dependent on whether officers judged actual truths or actual lies and on the method by which confidence was measured.
Lying aversion and prosocial behaviour
Biziou-van-Pol, Laura; Novaro, Arianna; Liberman, Andrés Occhipinti; Capraro, Valerio
2015-01-01
The focus of this paper is the moral conflict between lying aversion and prosociality. What does telling a white lie signal about a person's prosocial tendencies? How does believing a possibly untruthful message signal about a listener's prosocial tendencies? To answer these questions, we conducted a 2x3 experiment. In the first stage we measured altruistic tendencies using a Dictator Game and cooperative tendencies using a Prisoner's dilemma. In the second stage, we used a sender-receiver game to measure aversion to telling a Pareto white lie (i.e., a lie that helps both the liar and the listener), aversion to telling an altruistic white lie (i.e., a lie that helps the listener at the expense of the liar), and skepticism towards believing a possibly untruthful message. We found three major results: (i) both altruism and cooperation are positively correlated with aversion to telling a Pareto white lie; (ii) neither altruism nor cooperation are significantly correlated with aversion to telling an altruistic wh...
Cartan geometries and their symmetries a Lie algebroid approach
Crampin, Mike
2016-01-01
In this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle, and the connections on such groupoids together with their symmetries. We also see how the infinitesimal approach, using Lie algebroids rather than Lie groupoids, and in particular using Lie algebroids of vector fields along the projection of the fibre bundle, may be of benefit. We then introduce Cartan geometries, together with a number of tools we shall use to study them. We take, as particular examples, the four classical types of geometry: affine, projective, Riemannian and conformal geometry. We also see how our approach can start to fit into a more general theory. Finally, we specialize to the geometries (affine and projective) associated with path spaces and geodesics, and consider their symmetries and other properties.
k-Symplectic Lie systems: theory and applications
de Lucas, J.; Vilariño, S.
2015-03-01
A Lie system is a system of first-order ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields: a so-called Vessiot-Guldberg Lie algebra. We suggest the definition of a particular class of Lie systems, the k-symplectic Lie systems, admitting a Vessiot-Guldberg Lie algebra of Hamiltonian vector fields with respect to the presymplectic forms of a k-symplectic structure. We devise new k-symplectic geometric methods to study their superposition rules, t-independent constants of motion and general properties. Our results are illustrated through examples of physical and mathematical interest. As a byproduct, we find a new interesting setting of application of the k-symplectic geometry: systems of first-order ordinary differential equations.
Lies, Calculations and Constructions: Beyond How to Lie with Statistics
Best, Joel
2005-01-01
Darrell Huff’s How to Lie with Statistics remains the best-known, nontechnical call for critical thinking about statistics. However, drawing a distinction between statistics and lying ignores the process by which statistics are socially constructed. For instance, bad statistics often are disseminated by sincere, albeit innumerate advocates (e.g., inflated estimates for the number of anorexia deaths) or through research findings selectively highlighted to attract media coverage (e.g., a recent...
Last Multipliers on Lie Algebroids
Mircea Crasmareanu; Cristina-Elena Hreţcanu
2009-06-01
In this paper we extend the theory of last multipliers as solutions of the Liouville’s transport equation to Lie algebroids with their top exterior power as trivial line bundle (previously developed for vector fields and multivectors). We define the notion of exact section and the Liouville equation on Lie algebroids. The aim of the present work is to develop the theory of this extension from the tangent bundle algebroid to a general Lie algebroid (e.g. the set of sections with a prescribed last multiplier is still a Gerstenhaber subalgebra). We present some characterizations of this extension in terms of Witten and Marsden differentials.
Gravitating fluids with Lie symmetries
Msomi, A M; Maharaj, S D
2010-01-01
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means of Lie point symmetries. The method utilised reduces the partial differential equation to an ordinary differential equation according to the Lie symmetry admitted. We show that a class of solutions found previously can be characterised by a particular Lie generator. Several new families of solutions are found explicitly. In particular we find the relevant ordinary differential equation for all one-dimensional optimal subgroups; in several cases the ordinary differential equation can be solved in general. We are in a position to characterise particular solutions with a linear barotropic equation of state.
Historical Techniques of Lie Detection
Martina Vicianova
2015-08-01
Full Text Available Since time immemorial, lying has been a part of everyday life. For this reason, it has become a subject of interest in several disciplines, including psychology. The purpose of this article is to provide a general overview of the literature and thinking to date about the evolution of lie detection techniques. The first part explores ancient methods recorded circa 1000 B.C. (e.g., God’s judgment in Europe. The second part describes technical methods based on sciences such as phrenology, polygraph and graphology. This is followed by an outline of more modern-day approaches such as FACS (Facial Action Coding System, functional MRI, and Brain Fingerprinting. Finally, after the familiarization with the historical development of techniques for lie detection, we discuss the scope for new initiatives not only in the area of designing new methods, but also for the research into lie detection itself, such as its motives and regulatory issues related to deception.
Lie symmetry analysis of some time fractional partial differential equations
El Kinani, E. H.; Ouhadan, A.
2015-04-01
This paper uses Lie symmetry analysis to reduce the number of independent variables of time fractional partial differential equations. Then symmetry properties have been employed to construct some exact solutions.
Structure of Solvable Quadratic Lie Algebras
ZHU Lin-sheng
2005-01-01
@@ Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras.
Lie bialgebras of generalized Witt type
SONG; Guang'ai; SU; Yucai
2006-01-01
In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W (x) W) is trivial.
An evaluation on Real Semisimple Lie Algebras
无
2000-01-01
@@ The theory of Lie groups and Lie algebras stem from that of continuous groups founded by Sophus Lie at the end of 19th century. From the beginning, the theory of Lie groups and Lie algebras has displayed great value in both theoretical researches and applications.
Cohomology of Heisenberg Lie superalgebras
Bai, Wei; Liu, Wende
2017-02-01
Suppose the ground field to be algebraically closed and of characteristic different from 2 and 3. All Heisenberg Lie superalgebras consist of two super-versions of the Heisenberg Lie algebras, 𝔥2m,n and 𝔟𝔞n with m a non-negative integer and n a positive integer. The space of a "classical" Heisenberg Lie superalgebra 𝔥2m,n is the direct sum of a superspace with a non-degenerate anti-supersymmetric even bilinear form and a one-dimensional space of values of this form constituting the even center. The other super-analog of the Heisenberg Lie algebra, 𝔟𝔞n, is constructed by means of a non-degenerate anti-supersymmetric odd bilinear form with values in the one-dimensional odd center. In this paper, we study the cohomology of 𝔥2m,n and 𝔟𝔞n with coefficients in the trivial module by using the Hochschild-Serre spectral sequences relative to a suitable ideal. In the characteristic zero case, for any Heisenberg Lie superalgebra, we determine completely the Betti numbers and associative superalgebra structures for their cohomology. In the characteristic p > 3 case, we determine the associative superalgebra structure for the divided power cohomology of 𝔟𝔞n and we also make an attempt to determine the divided power cohomology of 𝔥2m,n by computing it in a low-dimensional case.
Langs, R
In this paper an attempt is made to conceptualize a basic dimension of various psychotherapeutic treatment modalities, especially psychoanalysis and psychoanalytically oriented psychotherapy. The central variable under consideration is the extent to which each endeavors to approach the truth within both patient and therapist as it exists dynamically in terms of their spiraling unconscious communicative interaction. That treatment modality which takes into account every possible dimension of such truths is termed truth therapy. Treatment modalities that make no attempt to arrive at these truths or that deliberately or inadvertently falsify their nature are termed lie or barrier therapies. Extensive consideration is given to truth therapy and the truth system on which it is based. The basis for the need for lie therapies is explored, and lie systems, which may arise from either patient or therapist, or both, are identified. A classification of common types of lie patients and lie therapists (and their main techniques) is offered. The implications of this delineation for our understanding of the dynamic therapies are discussed, and a number of new clinical issues arising from this perspective are addressed.
Antonio J Calderón Martín
2009-04-01
We begin the study of arbitrary split Lie triple systems by focussing on those with a coherent 0-root space. We show that any such triple systems with a symmetric root system is of the form $T=\\mathcal{U}+\\sum_j I_j$ with $\\mathcal{U}$ a subspace of the 0-root space $T_0$ and any $I_j$ a well described ideal of , satisfying $[I_j,T,I_k]=0$ if $j≠ k$. Under certain conditions, it is shown that is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity of is characterized. The key tool in this job is the notion of connection of roots in the framework of split Lie triple systems.
Loop Virasoro Lie conformal algebra
Wu, Henan, E-mail: wuhenanby@163.com; Chen, Qiufan; Yue, Xiaoqing [Department of Mathematics, Tongji University, Shanghai 200092 (China)
2014-01-15
The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.
Isomorphism of Intransitive Linear Lie Equations
Jose Miguel Martins Veloso
2009-11-01
Full Text Available We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.
Cartan Connections and Lie Algebroids
Michael Crampin
2009-06-01
Full Text Available This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A.D., Trans. Amer. Math. Soc. 358 (2006, 3651–3671], and tractor calculus [Cap A., Gover A.R., Trans. Amer. Math. Soc. 354 (2001, 1511–1548].
Cartan Connections and Lie Algebroids
Crampin, Michael
2009-01-01
This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A.D., Trans. Amer. Math. Soc. 358 (2006), 3651-3671], and tractor calculus [Cap A., Gover A.R., Trans. Amer. Math. Soc. 354 (2001), 1511-1548].
String Topology for Lie Groups
A. Hepworth, Richard
2010-01-01
In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a direct description of this Batalin-Vilkovisky algebra in the case that the manifold is a compact Lie group G. Our answer ...
Semiclassical states on Lie algebras
Tsobanjan, Artur, E-mail: artur.tsobanjan@gmail.com [King’s College, 133 North River Street, Kingston, Pennsylvania 18702 (United States)
2015-03-15
The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.
The Realization of 4-dimensional 3-Lie Algebras%4维3-Lie代数的实现
刘建波; 张艳艳; 张知学
2007-01-01
In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.
Symmetry via Lie algebra cohomology
Eastwood, Michael
2010-01-01
The Killing operator on a Riemannian manifold is a linear differential operator on vector fields whose kernel provides the infinitesimal Riemannian symmetries. The Killing operator is best understood in terms of its prolongation, which entails some simple tensor identities. These simple identities can be viewed as arising from the identification of certain Lie algebra cohomologies. The point is that this case provides a model for more complicated operators similarly concerned with symmetry.
Can Lies Be Detected Unconsciously?
David eShanks
2015-08-01
Full Text Available People are typically poor at telling apart truthful and deceptive statements. Based on the Unconscious Thought Theory, it has been suggested that poor lie detection arises from the intrinsic limitations of conscious thinking and can be improved by facilitating the contribution of unconscious thought. In support of this hypothesis, Reinhard, Greifeneder, and Scharmach (2013 observed improved lie detection among participants engaging in unconscious thought. The present study aimed to replicate this unconscious thought advantage using a similar experimental procedure but with an important improvement in a key control condition. Specifically, participants judged the truthfulness of 8 video recordings in three thinking modes: immediately after watching them or after a period of unconscious or conscious deliberation. Results from two experiments (combined N = 226 failed to reveal a significant difference in lie detection accuracy between the thinking modes, even after efforts were made to facilitate the occurrence of an unconscious thought advantage in Experiment 2. The results imply that the unconscious thought advantage in deception detection is not a robust phenomenon.
Particle-like structure of Lie algebras
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.
Filiform Lie algebras of order 3
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.
Transformation groups and Lie algebras
Ibragimov, Nail H
2013-01-01
This book is based on the extensive experience of teaching for mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in the book provide universal and effective method for solving nonlinear differential equations analytically. Introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter.
Controllability of Linear Systems with inner derivation on Lie Groups
Jouan, Philippe
2011-01-01
A vector field on a connected Lie group is said to be linear if its flow is a one parameter group of automorphisms. A control-affine system is linear if the drift is linear and the controlled vector fields right invariant. The controllability properties of such systems are studied, mainly in the case where the derivation of the group Lie algebra that can be associated to the linear vector field is inner. After some general considerations controllability properties on semi simple, nilpotent an...
Emergence of Lying in Very Young Children
Evans, Angela D.; Lee, Kang
2013-01-01
Lying is a pervasive human behavior. Evidence to date suggests that from the age of 42 months onward, children become increasingly capable of telling lies in various social situations. However, there is limited experimental evidence regarding whether very young children will tell lies spontaneously. The present study investigated the emergence of…
A Kind of Braided-Lie Structures
无
2003-01-01
@@ We introduce a family of braidedLie algebras.They are Lie algebras in the unifying YetterDrinfeldLong module categoryJJMQQ where J and Q are Hopf algebras.We study their structure and the braidedLie structure of an algebra A in JJM QQ.
Probability on real Lie algebras
Franz, Uwe
2016-01-01
This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.
Dobrev, V K
2013-01-01
In the present paper we continue the project of systematic construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we call 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduce the new notion of {\\it parabolic relation} between two non-compact semisimple Lie algebras g and g' that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra E_{7(7)} which is parabolically related to the CLA E_{7(-25)}, the parabolic subalgebras including E_{6(6)} and E_{6(-6)} . Other interesting examples are the orthogonal algebras so(p,q) all of which are parabolically related to the conformal algebra so(n,2) with p+q=n+2, the parabolic subalgebras including the Lorentz subalgebra so(n-1,1) and its analogs so(p-1,...
Construction of Difference Equations Using Lie Groups
Axford, R.A.
1998-08-01
The theory of prolongations of the generators of groups of point transformations to the grid point values of dependent variables and grid spacings is developed and applied to the construction of group invariant numerical algorithms. The concepts of invariant difference operators and generalized discrete sources are introduced for the discretization of systems of inhomogeneous differential equations and shown to produce exact difference equations. Invariant numerical flux functions are constructed from the general solutions of first order partial differential equations that come out of the evaluation of the Lie derivatives of conservation forms of difference schemes. It is demonstrated that invariant numerical flux functions with invariant flux or slope limiters can be determined to yield high resolution difference schemes. The introduction of an invariant flux or slope limiter can be done so as not to break the symmetry properties of a numerical flux-function.
Konkurentideta lennukokad / Martin Hanson
Hanson, Martin, 1984-
2008-01-01
Airo Catering Services toodab lennukitel toitlustamiseks umbes kaks miljonit söögikorda aastas. Vt. samas: Äriklassile kaetakse rikkalikum toidulaud; Piloot ja kapten söövad eri toitu. Diagramm: Airo Cateringi majandustulemused
Norma kaotamine / Martin Hanson
Hanson, Martin, 1984-
2010-01-01
Autoturvasüsteemide tootjale Autolivile kuulub tütarfirma Automotive Holdingu kaudu 51% Norma aktsiatest, kuid plaanitakse tõsta osalust 77%-ni. Väikeaktsionärid kaaluvad Autolivi pakkumist, kuid kui Autoliv saab nõusoleku vähemalt 39% omanikelt, peavad ka teised oma aktsiad loovutama. Autolivi pakutud ülevõtmishinnaks on 92,31 krooni ja see tekitab väikeaktsionärides ning analüütikutes vastakaid tundeid. Tabel
Norma kaotamine / Martin Hanson
Hanson, Martin, 1984-
2010-01-01
Autoturvasüsteemide tootjale Autolivile kuulub tütarfirma Automotive Holdingu kaudu 51% Norma aktsiatest, kuid plaanitakse tõsta osalust 77%-ni. Väikeaktsionärid kaaluvad Autolivi pakkumist, kuid kui Autoliv saab nõusoleku vähemalt 39% omanikelt, peavad ka teised oma aktsiad loovutama. Autolivi pakutud ülevõtmishinnaks on 92,31 krooni ja see tekitab väikeaktsionärides ning analüütikutes vastakaid tundeid. Tabel
Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group $H_4$
Eghbali, A
2015-01-01
We show that the WZW model on the Heisenberg Lie group $H_4$ has Poisson-Lie symmetry only when the dual Lie group is ${ A}_2 \\oplus 2{ A}_1$. In this way, we construct the mutual T-dual sigma models on Drinfel'd double generated by the Heisenberg Lie group $H_4$ and its dual pair, ${ A}_2 \\oplus 2{ A}_1$, as the target space in such a way that the original model is the same as the $H_4$ WZW model. Furthermore, we show that the dual model is conformal up to two loops order. Finally, we discuss $D$-branes and the worldsheet boundary conditions defined by a gluing matrix on the $H_4$ WZW model. Using the duality map obtained from the canonical transformation description of the Poisson-Lie T-duality transformations for the gluing matrix which locally defines the properties of the $D$-brane, we find two different cases of the gluing matrices for the WZW model based on the Heisenberg Lie group $H_4$ and its dual model.
Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group H4
A. Eghbali
2015-10-01
Full Text Available We show that the WZW model on the Heisenberg Lie group H4 has Poisson–Lie symmetry only when the dual Lie group is A2⊕2A1. In this way, we construct the mutual T-dual sigma models on Drinfel'd double generated by the Heisenberg Lie group H4 and its dual pair, A2⊕2A1, as the target space in such a way that the original model is the same as the H4 WZW model. Furthermore, we show that the dual model is conformal up to two-loop order. Finally, we discuss D-branes and the worldsheet boundary conditions defined by a gluing matrix on the H4 WZW model. Using the duality map obtained from the canonical transformation description of the Poisson–Lie T-duality transformations for the gluing matrix which locally defines the properties of the D-brane, we find two different cases of the gluing matrices for the WZW model based on the Heisenberg Lie group H4 and its dual model.
Lies and Deception: A Failed Reconciliation
Broncano-Berrocal, Fernando
2013-01-01
The traditional view of lying says that lying is a matter of intending to deceive others by making statements that one believes to be false. Jennifer Lackey has recently defended the following version of the traditional view: A lies to B just in case (i) A states that p to B, (ii) A believes that...... is false and (iii) A intends to be deceptive to B in stating that p. I argue that, despite all the virtues that Lackey ascribes to her view, conditions (i), (ii) and (iii) are not sufficient for lying.......The traditional view of lying says that lying is a matter of intending to deceive others by making statements that one believes to be false. Jennifer Lackey has recently defended the following version of the traditional view: A lies to B just in case (i) A states that p to B, (ii) A believes that p...
The Virasoro Algebra and Some Exceptional Lie and Finite Groups
Michael P. Tuite
2007-01-01
Full Text Available We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series of simple Lie groups and some exceptional finite simple groups including the Monster and Baby Monster.
2007-01-01
Jõekääru Jazz'ile järgneval nädalal tõi ürituse peakorraldaja Allan Liik toimetusse seal esinenud muusikud. Vestlusringis olid: Allan Liik, Hedvig Hanson, Andre Maaker, Ain Agan, Raivo Tafenau ja Sergio Bastos
2007-01-01
Jõekääru Jazz'ile järgneval nädalal tõi ürituse peakorraldaja Allan Liik toimetusse seal esinenud muusikud. Vestlusringis olid: Allan Liik, Hedvig Hanson, Andre Maaker, Ain Agan, Raivo Tafenau ja Sergio Bastos
[Psychopathological study of lie motif in schizophrenia].
Otsuka, Koichiro; Kato, Satoshi
2006-01-01
The theme of a statement is called "lie motif" by the authors when schizophrenic patients say "I have lied to anybody". We tried to analyse of the psychopathological characteristics and anthropological meanings of the lie motifs in schizophrenia, which has not been thematically examined until now, based on 4 cases, and contrasting with the lie motif (Lügenmotiv) in depression taken up by A. Kraus (1989). We classified the lie motifs in schizophrenia into the following two types: a) the past directive lie motif: the patients speak about their real lie regarding it as a 'petty fault' in their distant past with self-guilty feeling, b) the present directive lie motif: the patients say repeatedly 'I have lied' (about their present speech and behavior), retreating from their previous commitments. The observed false confessions of innocent fault by the patients seem to belong to the present directed lie motif. In comparison with the lie motif in depression, it is characteristic for the lie motif in schizophrenia that the patients feel themselves to already have been caught out by others before they confess the lie. The lie motif in schizophrenia seems to come into being through the attribution process of taking the others' blame on ones' own shoulders, which has been pointed out to be common in the guilt experience in schizophrenia. The others' blame on this occasion is due to "the others' gaze" in the experience of the initial self-centralization (i.e. non delusional self-referential experience) in the early stage of schizophrenia (S. Kato 1999). The others' gaze is supposed to bring about the feeling of amorphous self-revelation which could also be regarded as the guilt feeling without content, to the patients. When the guilt feeling is bound with a past concrete fault, the patients tell the past directive lie motif. On the other hand, when the patients cannot find a past fixed content, and feel their present actions as uncertain and experience them as lies, the
Learning to lie: Effects of practice on the cognitive cost of lying
Bram eVan Bockstaele
2012-11-01
Full Text Available Cognitive theories on deception posit that lying requires more cognitive resources than telling the truth. In line with this idea, it has been demonstrated that deceptive responses are typically associated with increased response times and higher error rates compared to truthful responses. Although the cognitive cost of lying has been assumed to be resistant to practice, it has recently been shown that people who are trained to lie can reduce this cost. In the present study (n = 42, we further explored the effects of practice on one’s ability to lie by manipulating the proportions of lie and truth-trials in a Sheffield lie test across three phases: Baseline (50% lie, 50% truth, Training (frequent-lie group: 75% lie, 25% truth; control group: 50% lie, 50% truth; and frequent-truth group: 25% lie, 75% truth, and Test (50% lie, 50% truth. The results showed that lying became easier while participants were trained to lie more often and that lying became more difficult while participants were trained to tell the truth more often. Furthermore, these effects did carry over to the test phase, but only for the specific items that were used for the training manipulation. Hence, our study confirms that relatively little practice is enough to alter the cognitive cost of lying, although this effect does not persist over time for non-practiced items.
di Battista, Patrick
1997-01-01
Examines whether a lie's cognitive representation affects deceivers' ability to respond to probing. Shows that behavioral changes made in response to probing varied depending on whether the lie was a familiar lie or an unfamiliar lie but that none of these behaviors were related to judges' ratings of truthfulness. (SR)
Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
Chryssomalakos, Chryssomalis
2007-01-01
We present a star product for noncommutative spaces of Lie type, including the so called ``canonical'' case by introducing a central generator, which is compatible with translations and admits a simple, manageable definition of an invariant integral. A quasi-cyclicity property for the latter is shown to hold, which reduces to exact cyclicity when the adjoint representation of the underlying Lie algebra is traceless. Several explicit examples illuminate the formalism, dealing with kappa-Minkowski spacetime and the Heisenberg algebra (``canonical'' noncommutative 2-plane).
Quantum Lie theory a multilinear approach
Kharchenko, Vladislav
2015-01-01
This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev operations for the Lie theory of nonassociative products. Opening with an introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.
Lie-series for orbital elements -- II. The spatial case
Pál, András
2016-01-01
If one has to attain high accuracy over long timescales during the numerical computation of the N-body problem, the method called Lie-integration is one of the most effective algorithms. In this paper we present a set of recurrence relations with which the coefficients needed by the Lie-integration of the orbital elements related to the spatial N-body problem can be derived up to arbitrary order. Similarly to the planar case, these formulae yields identically zero series in the case of no perturbations. In addition, the derivation of the formulae has two stages, analogously to the planar problem. Namely, the formulae are obtained to the first order, and then, higher order relations are expanded by involving directly the multilinear and fractional properties of the Lie-operator.
3-Leibniz bialgebras (3-Lie bialgebras)
2016-01-01
In this paper by use of cohomology complex of $3$-Leibniz algebras, the definitions of Leibniz bialgebras (and Lie bialgebras) are extended for the case of $3$-Leibniz algebras. Many theorems about Leibniz bialgebras are extended and proved for the case of $3$-Leibniz bialgebras ($3$-Lie bialgebras). Moreover a new theorem on the correspondence between $3$-Leibniz bialgebra and its associated Leibniz bialgebra is proved. $3$-Lie bialgebra as particular case of the $3$-Leibniz bialgebra is inv...
Killing Forms of Isotropic Lie Algebras
Malagon, Audrey
2010-01-01
This paper presents a method for computing the Killing form of an isotropic Lie algebra defined over an arbitrary field based on the Killing form of a subalgebra containing its anisotropic kernel. This approach allows for streamlined formulas for many Lie algebras of types E6 and E7 and yields a unified formula for all Lie algebras of inner type E6, including the anisotropic ones.
ALIED: A Theory of Lie Detection
Chris N. H. Street
2016-07-01
Full Text Available We are very inaccurate lie detectors, and tend to believe what others tell us is the truth more often than we ought to. In fact, studies on lie detection typically describe our tendency to believe others as an error in judgment. Although people may look like hopeless lie detectors, the Adaptive Lie Detector theory (ALIED claims that people are actually making smart, informed judgments. This article explores the ALIED theory and what it means for those wanting to spot a liar.
Computations in finite-dimensional Lie algebras
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.
Some Remarks Concerning the Invariants of Rank One Solvable Real Lie Algebras
Rutwig Campoamor-Stursberg
2005-01-01
A corrected and completed list of six dimensional real Lie algebras with five dimensional nilradical is presented. Their invariants for the coadjoint representation are computed and some results on the invariants of solvable Lie algebras in arbitrary dimension whose nilradical has codimension one are also given. Specifically, it is shown that any rank one solvable Lie algebra of dimension n without invariants determines a family of (n +2k)-dimensional algebras with the same property.
The Lie algebra of the N=2-string
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.)
The structure of complex Lie groups
Lee, Dong Hoon
2001-01-01
Complex Lie groups have often been used as auxiliaries in the study of real Lie groups in areas such as differential geometry and representation theory. To date, however, no book has fully explored and developed their structural aspects.The Structure of Complex Lie Groups addresses this need. Self-contained, it begins with general concepts introduced via an almost complex structure on a real Lie group. It then moves to the theory of representative functions of Lie groups- used as a primary tool in subsequent chapters-and discusses the extension problem of representations that is essential for studying the structure of complex Lie groups. This is followed by a discourse on complex analytic groups that carry the structure of affine algebraic groups compatible with their analytic group structure. The author then uses the results of his earlier discussions to determine the observability of subgroups of complex Lie groups.The differences between complex algebraic groups and complex Lie groups are sometimes subtle ...
Testosterone Administration Reduces Lying in Men
Wibral, M.; Dohmen, T.J.; Klingmüller, Dietrich; Weber, Bernd; Falk, Armin
2012-01-01
Lying is a pervasive phenomenon with important social and economic implications. However, despite substantial interest in the prevalence and determinants of lying, little is known about its biological foundations. Here we study a potential hormonal influence, focusing on the steroid hormone
Lie Group Techniques for Neural Learning
2005-01-03
Lie group techniques for Neural Learning Edinburgh June 2004 Elena Celledoni SINTEF Applied Mathematics, IMF-NTNU Lie group techniques for Neural...ORGANIZATION NAME(S) AND ADDRESS(ES) SINTEF Applied Mathematics, IMF-NTNU 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND
The Killing Forms of Lie Triple Systems
ZHANG Zhi Xue; GAO Rui
2009-01-01
For Lie triple systems in the characteristic zero setting, we obtain by means of the Killing forms two criterions for semisimplicity and for solvability respectively, and then investigate the relationship among the Killing forms of a real Lie triple system To, the complexification T of To, and the realification of T.
Matrix Lie Algebras and Integrable Couplings
ZHANG Yu-Feng; GUO Fu-Kui
2006-01-01
Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively.
On Nambu-Lie 3-algebra representations
Sochichiu, Corneliu
2008-01-01
We propose a recipe to construct matrix representations of Nambu--Lie 3-algebras in terms of irreducible representations of underlying Lie algebra. The case of Euclidean four-dimensional 3-algebra is considered in details. We find that representations of this 3-algebra are not possible in terms of only Hermitian matrices in spite of its Euclidean nature.
Computations in finite-dimensional Lie algebras
Cohen, A.M.; Graaf, W.A. de; Rónyai, L.
2001-01-01
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 packagecan be found in Cohen and de Graaf[1]. Since then, in a collaborative
Lie symmetries and 2D Material Physics
Belhaj, Adil
2014-01-01
Inspired from Lie symmetry classification, we establish a correspondence between rank two Lie symmetries and 2D material physics. The material unit cell is accordingly interpreted as the geometry of a root system. The hexagonal cells, appearing in graphene like models, are analyzed in some details and are found to be associated with A_2 and G_2 Lie symmetries. This approach can be applied to Lie supersymmetries associated with fermionic degrees of freedom. It has been suggested that these extended symmetries can offer a new way to deal with doping material geometries. Motivated by Lie symmetry applications in high energy physics, we speculate on a possible connection with (p,q) brane networks used in the string theory compactification on singular Calabi-Yau manifolds.
Characteristics of the Eysenck Personality Questionnaire Lie Scale and of Extreme Lie Scorers.
Loo, Robert
1980-01-01
Results of statistical analyses suggest that high lie-scorers respond honestly, and that the Lie Scale for the Eysenck Personality Inventory may reflect a personality dimension of interest rather than an extraneous and undesirable factor to be eliminated. (Author)
M2 to D2 and vice versa by 3-Lie and Lie bialgebra
Aali-Javanangrouh, M.; Rezaei-Aghdam, A. [Azarbaijan Shahid Madani University, Department of Physics, Faculty of Science, Tabriz (Iran, Islamic Republic of)
2016-11-15
Using the concept of a 3-Lie bialgebra, which has recently been defined in arXiv:1604.04475, we construct a Bagger-Lambert-Gustavson (BLG) model for the M2-brane on a Manin triple of a special 3-Lie bialgebra. Then by using the correspondence and the relation between those 3-Lie bialgebra with Lie bialgebra, we reduce this model to an N = (4,4) WZW model (D2-brane), such that its algebraic structure is a Lie bialgebra with one 2-cocycle. In this manner by using the correspondence of the 3-Lie bialgebra and Lie bialgebra (for this special 3-Lie algebra) one can construct the M2-brane from a D2-brane and vice versa. (orig.)
A-扩张Lie Rinehart代数%On the A-extended Lie Rinehart Algebras
陈酌; 祁玉海
2007-01-01
The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary,commutative, associative algebra A. It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group, analogous to the well known relationship of Lie algebras and Lie groups.
The Prevalence of Lying in America: Three Studies of Self-Reported Lies
Serota, Kim B.; Levine, Timothy R.; Boster, Franklin J.
2010-01-01
This study addresses the frequency and the distribution of reported lying in the adult population. A national survey asked 1,000 U.S. adults to report the number of lies told in a 24-hour period. Sixty percent of subjects report telling no lies at all, and almost half of all lies are told by only 5% of subjects; thus, prevalence varies widely and…
Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
Movshev, M.V. [Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651 (United States); Schwarz, A., E-mail: schwarz@math.ucdavis.edu [Department of Mathematics, University of California, Davis, CA 95616 (United States); Xu, Renjun [Department of Physics, University of California, Davis, CA 95616 (United States)
2012-01-11
We study the homology and cohomology groups of super Lie algebras of supersymmetries and of super Poincare Lie algebras in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions {<=}11. For dimensions D=10,11 we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry Lie algebras.
Elementary n-Lie Algebras%基本n-Lie代数
白瑞蒲; 张艳艳
2007-01-01
In this paper, we mainly study some properties of elementary n-Lie algebras, and prove some necessary and sufficient conditions for elementary n-Lie algebras. We also give the relations between elementary n-algebras and E-algebras.
A Class of Solvable Lie Algebras and Their Hom-Lie Algebra Structures
LI Xiao-chao; LI Dong-ya; JIN Quan-qin
2014-01-01
The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1 as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1. Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.
AGN identification: what lies ahead
Fotopoulou, Sotiria
2016-08-01
Classification has been one the first concerns of modern astronomy, starting from stars sorted in the famous Harvard classification system and promptly followed by the morphological classification of galaxies by none other than Edwin Hubble himself (Hubble 1926). Both classification schema are essentially connected to the physics of the objects reflecting the temperature for stars and e.g. the age of the star population for galaxies. Systematic observations of galaxies have revealed the intriguing class of Active Galactic Nuclei (AGN), objects of tremendous radiation that do not share the same properties of what we now call normal galaxies. Observations have led to the definition of distinct and somewhat arbitrary categories (Seyfert galaxies, quasars, QSO, radio AGN, etc), essentially rediscovering the many faces of the same phenomenon, up until the unification of AGN (Antonucci 1993, Urry and Padovani 1995). Even after the realization that all AGN have the same engine powering their amazing radiation, astronomers are still using and refining the selection criteria within their favorite electromagnetic range in the hope to better understand the impact of the AGN phenomenon in the greater context of galaxy evolution. In the dawn of Big Data astronomy we find ourselves equipped with new tools. I will present the prospects of machine learning methods in better understanding the AGN population. Namely, I will show results from supervised learning algorithms whereby a labeled training set is used to amalgamate decision tree(s) (Fotopoulou et al., 2016) or neural network(s), and unsupervised learning where the algorithm performs clustering analysis of the full dataset in a multidimensional space identifying clusters of objects sharing potentially the same physical properties (Fotopoulou in prep.).
Expansion in finite simple groups of Lie type
Tao, Terence
2015-01-01
Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.
A New Type of Fractional Lie Symmetrical Method and its Applications
Zhang, Xiao-Tian; He, Jin-Man; Luo, Shao-Kai
2017-03-01
In this paper, we present a new type of fractional Lie symmetrical method for finding conserved quantities and explore its applications. For the fractional generalized Hamiltonian system, we introduce a new kind of single-parameter fractional infinitesimal transformation of Lie group in α-1 order space and, under this transformation, give the invariance of the fractional dynamical system and the fractional Lie symmetrical determining equation. Further, a number of important relationships of the fractional Lie symmetrical method are investigated, which reveal the interior properties of the system. By using these relationships, a fractional Lie symmetrical basic integral variable relation and a new fractional Lie symmetrical conservation law are presented. The new conserved quantity is constructed base on fractional Lie symmetrical infinitesimal generators and the interior properties of the system itself, without solving the complicated structural equation. Furthermore, the fractional Lie symmetrical method is applied to the fractional generalized Hamiltonian system of even dimensions. Also, as the new fractional Lie symmetrical method's applications, we respectively find the conserved quantities of a fractional Duffing oscillator model and a fractional Lotka biochemical oscillator model.
Introduction to the theory of Lie groups
Godement, Roger
2017-01-01
This textbook covers the general theory of Lie groups. By first considering the case of linear groups (following von Neumann's method) before proceeding to the general case, the reader is naturally introduced to Lie theory. Written by a master of the subject and influential member of the Bourbaki group, the French edition of this textbook has been used by several generations of students. This translation preserves the distinctive style and lively exposition of the original. Requiring only basics of topology and algebra, this book offers an engaging introduction to Lie groups for graduate students and a valuable resource for researchers.
Quasi-big\\`ebres de Lie et cohomologie d'alg\\`ebre de Lie
Bangoura, Momo
2010-01-01
Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, \\mu, \\gamma ,\\phi ?), correspond one Lie algebra structure on D = G\\oplus G*, called the double of the given Lie quasi-bialgebra. We show that there exist on \\Lambda G, the exterior algebra of G, a D-module structure and we establish an isomorphism of D-modules between \\Lambda D and End(\\Lambda G), D acting on \\Lambda D by the adjoint action.
Induced Lie Algebras of a Six-Dimensional Matrix Lie Algebra
ZHANG Yu-Feng; LIU Jing
2008-01-01
By using a six-dimensional matrix Lie algebra [Y.F. Zhang and Y. Wang, Phys. Lett. A 360 (2006) 92], three induced Lie algebras are constructed. One of them is obtained by extending Lie bracket, the others are higher-dimensional complex Lie algebras constructed by using linear transformations. The equivalent Lie algebras of the later two with multi-component forms are obtained as well. As their applications, we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations.
Permutation Weights and Modular Poincare Polynomials for Affine Lie Algebras
Gungormez, M
2010-01-01
Poincare Polynomial of a Kac-Moody Lie algebra can be obtained by classifying the Weyl orbit $W(\\rho)$ of its Weyl vector $\\rho$. A remarkable fact for Affine Lie algebras is that the number of elements of $W(\\rho)$ is finite at each and every depth level though totally it has infinite number of elements. This allows us to look at $W(\\rho)$ as a manifold graded by depths of its elements and hence a new kind of Poincare Polynomial is defined. We give these polynomials for all Affine Kac-Moody Lie algebras, non-twisted or twisted. The remarkable fact is however that, on the contrary to the ones which are classically defined,these new kind of Poincare polynomials have modular properties, namely they all are expressed in the form of eta-quotients. When one recalls Weyl-Kac character formula for irreducible characters, it is natural to think that this modularity properties could be directly related with Kac-Peterson theorem which says affine characters have modular properties. Another point to emphasize is the rel...
The Frattini Subalgebra of Restricted Lie Superalgebras
Liang Yun CHEN; Dao Ji MENG; Yong Zheng ZHANG
2006-01-01
In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra (L, [p]). We show first that if L = A1 (⊙) A2 (⊙) … (⊙) An, then φp (L) = φp (A1) + φp (A2) +… +φp (An),where each Ai is a p-ideal of L. We then obtain two results: F(L) = φ(L) = J(L) = L(1) if and only if L is nilpotent; Fp(L) and F(L) are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for φp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.
Stunkard, H.W.; Uzmann, J.R.
1959-01-01
ano,nalus, taken at Cerros Island, Mexico. Hanson ( 1950) identified two specimens collected from Calamus sp. at Bermuda by the late F. D. Barker as Distontuni subtenue Linton, 1907, a species described originally from Calantus calanius in the same area. Comparison of these specimens with those from Tortugas identified by Manter as P. erythraeus established their identity, and P. erythraeus was suppressed as a synonym of Proctoeces subtenue (Linton, 1907). Hanson corrected the statement of Manter (1947), noting that it is the vitellaria, not the uterus, which never extends into the post testicular region.
Linearization from Complex Lie Point Transformations
Sajid Ali
2014-01-01
Full Text Available Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs which have Lie algebras of maximum dimension d, with d≤4. We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. Furthermore we provide a geometrical construction of the procedure adopted that provides an analogue in R3 of the linearizability criteria in R2.
Lie Superalgebras arising from bosonic representation
Jing, Naihuan
2012-01-01
A 2-toroidal Lie superalgebra is constructed using bosonic fields and a ghost field. The superalgebra contains $osp(1|2n)^{(1)}$ as a distinguished subalgebra and behaves similarly to the toroidal Lie superalgebra of type $B(0, n)$. Furthermore this algebra is a central extension of the algebra $osp(1|2n)\\otimes \\mathbb C[s, s^{-1}, t,t^{-1}]$.
Noncommutative geometry with graded differential Lie algebras
Wulkenhaar, Raimar
1997-06-01
Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the Connes-Lott prescription of noncommutative geometry, differs from that, however, by the implementation of unitary Lie algebras instead of associative * -algebras. The general scheme is presented in detail and is applied to functions ⊗ matrices.
Constructing semisimple subalgebras of semisimple Lie algebras
de Graaf, Willem A
2010-01-01
Algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple Lie algebra, up to linear equivalence. The algorithms have been used to obtain classifications of the semisimple subalgebras of the simple Lie algebras of ranks <= 8. These have been made available as a database inside the SLA package of GAP4. The subalgebras in this database are explicitly given, as well as the inclusion relations among them.
Lie Admissible Non-Associative Algebras
H.Mohammad Ahmadi; Ki-Bong Nam; Jonathan Pakinathan
2005-01-01
A non-associative ring which contains a well-known associative ring or Lie ring is interesting. In this paper, a method to construct a Lie admissible non-associative ring is given; a class of simple non-associative algebras is obtained; all the derivations of the non-associative simple N0,0,1 algebra defined in this paper are determined; and finally, a solid algebra is defined.
Central extension of graded Lie algebras
Welte, Angelika
2010-01-01
In this thesis we describe the universal central extension of two important classes of so-called root-graded Lie algebras defined over a commutative associative unital ring $k.$ Root-graded Lie algebras are Lie algebras which are graded by the root lattice of a locally finite root system and contain enough $\\mathfrak{sl}_2$-triples to separate the homogeneous spaces of the grading. Examples include the infinite rank analogs of the simple finite-dimensional complex Lie algebras. \\\\ In the thesis we show that in general the universal central extension of a root-graded Lie algebra $L$ is not root-graded anymore, but that we can measure quite easily how far it is away from being so, using the notion of degenerate sums, introduced by van der Kallen. We then concentrate on root-graded Lie algebras which are graded by the root systems of type $A$ with rank at least 2 and of type $C$. For them one can use the theory of Jordan algebras.
B-sub-modules of Lie(G)/Lie(B) and Smooth Schubert Varieties in G/B
Carrell, James B
2010-01-01
Let G be a complex semi-simple linear algebraic group without G_2 factors, B a Borel subgroup of G and T a maximal torus in B. The flag variety G/B is a projective G-homogeneous variety whose tangent space at the identity coset is isomorphic, as a B-module, to Lie(G)/Lie(B). Recall that if w is an element of the Weyl group W of the pair (G,T), the Schubert variety X(w) in G/B is by definition the closure of the Bruhat cell BwB. In this note we prove that X(w) is non-singular iff the following two conditions hold: 1) its Poincar\\'e polynomial is palindromic and 2) the tangent space TE(X(w)) to the set T-stable curves in X(w) through the identity is a $B$-submodule of Lie(G)/Lie(B). This gives two criteria in terms of the combinatorics of W which are necessary and sufficient for X(w) to be smooth: \\sum_{x\\le w} t^{\\ell(x)} is palindromic, and every root of (G,T) in the convex hull of the set of negative roots whose reflection is less than w (in the Bruhat order on W) has the property that its T-weight space (in...
A twisted generalization of Lie-Yamaguti algebras
Gaparayi, Donatien
2010-01-01
A twisted generalization of Lie-Yamaguti algebras, called Hom-Lie-Yamaguti algebras, is defined. Hom-Lie-Yamaguti algebras generalize Hom-Lie triple systems (and susequently ternary Hom-Nambu algebras) and Hom-Lie algebras in the same way as Lie-Yamaguti algebras generalize Lie triple systems and Lie algebras. It is shown that the category of Hom-Lie-Yamaguti algebras is closed under twisting by self-morphisms. Constructions of Hom-Lie-Yamaguti algebras from classical Lie-Yamaguti algebras and Malcev algebras are given. It is observed that, when the ternary operation of a Hom-Lie-Yamaguti algebra expresses through its binary one in a specific way, then such a Hom-Lie-Yamaguti algebra is a Hom-Malcev algebra.
Detecting true lies:police officers' ability to detect suspects' lies
Mann, Samantha; Vrij, Aldert; Bull, Ray
2004-01-01
Ninety-nine police officers, not identified in previous research as belonging to groups which are superior in lie detection, attempted to detect truths and lies told by suspects during their videotaped police interviews. Accuracy rates were higher than typically found in deception research and reached levels similar to those obtained by specialized lie detectors in previous research. Accuracy was positively correlated with perceived experience in interviewing suspects and with mentioning cues...
Inverse Limits in Representations of a Restricted Lie Algebra
Yu Feng YAO; Bin SHU; Yi Yang LI
2012-01-01
Let (g,[p]) be a restricted Lie algebra over an algebraically closed field of characteristic p ＞ 0.Then the inverse limits of "higher" reduced enveloping algebras {uxs (g) | s ∈ N} with x running over g* make representations of g split into different "blocks".In this paper,we study such an infinitedimensional algebra (A)x(g):=lim← Uxs (g) for a given x ∈ g*.A module category equivalence is built between subcategories of U(g)-mod and (A)x(g)-mod.In the case of reductive Lie algebras,(quasi)generalized baby Verma modules and their properties are described.Furthermore,the dimensions of projective covers of simple modules with characters of standard Levi form in the generalized x-reduced module category are precisely determined,and a higher reciprocity in the case of regular nilpotent is obtained,generalizing the ordinary reciprocity.
A unified study of orthogonal polynomials via Lie algebra
Pathan, M. A.; Agarwal, Ritu; Jain, Sonal
2017-02-01
In this paper, we discuss some operators defined on Lie algebras for the purpose of deriving properties of some special functions. The method developed in this paper can also be used to study some other special functions of mathematical physics. We have established a general theorem concerning eigenvectors for the product of two operators defined on a Lie algebra of endomorphisms of a vector space. Further, using this result, we have obtained differential recurrence relations and differential equations for the extended Jacobi polynomials and the Gegenbauer polynomials. Results of many researchers; see for example Radulescu (1991), Mandal (1991), Pathan and Khan (2003), Humi, and the references therein, follow as special cases of our results.
Classical Mechanics on Noncommutative Space with Lie-algebraic Structure
Miao, Yan-Gang; Yu, Shao-Jie
2009-01-01
We investigate the kinetics of a particle exerted by a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained in general due to some algebraic properties, such as the antisymmetry and Jacobi identity. Through solving the constraint equations the structure constants satisfy, we obtain two general sorts of algebraic structures, each of which corresponds to one type of noncommutative spaces. Based on such types of noncommutative spaces as the starting point, we analyze the classical motion of the particle by means of the Hamiltonian formalism defined on a Poisson manifold. Our results {\\em not only} include that of a recent work as our special cases, {\\em but also} provide new trajectories of motion governed mainly by marvelous extra forces. The extra forces with the unimaginable $t\\dot{x}$-, $\\dot{(xx)}$-, and $\\ddot{(xx)}$-dependence besides with the usual $t$-, $x$-, and $\\dot{x}$-dependence, originating...
Sati, Hisham
2015-01-01
We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of higher parameterized WZW-type sigma-models this naturally lifts to a Lie (p+1)-algebra structure on the Noether currents themselves. Applied to the Green-Schwarz-type action functionals for super p-brane sigma-models this yields super Lie (p+1)-algebra refinements of the traditional BPS brane charge extensions of supersymmetry algebras. We discuss this in the generality of higher differential geometry, where it applies also to branes with (higher) gauge fields on their worldvolume. Applied to the M5-brane sigma-model we recover and properly globalize the M-theory super Lie algebra extension of 11-dimensional superisometries by 2-brane and 5-brane charges. Passing beyond the infinitesimal Lie theory we find cohomological corrections to these charges in higher analogy to the familiar corrections for D-brane...
Riemannian manifolds as Lie-Rinehart algebras
Pessers, Victor; van der Veken, Joeri
2016-07-01
In this paper, we show how Lie-Rinehart algebras can be applied to unify and generalize the elementary theory of Riemannian geometry. We will first review some necessary theory on a.o. modules, bilinear forms and derivations. We will then translate some classical theory on Riemannian geometry to the setting of Rinehart spaces, a special kind of Lie-Rinehart algebras. Some generalized versions of classical results will be obtained, such as the existence of a unique Levi-Civita connection, inducing a Levi-Civita connection on a submanifold, and the construction of spaces with constant sectional curvature.
Jardino, Sergio
2010-01-01
We extend the concept of a generalized Lie 3-algebra, known to octonions $\\mathbb{O}$, to split-octonions $\\mathbb{SO}$. In order to do that, we introduce a notational device that unifies the two elements product of both of the algebras. We have also proved that $\\mathbb{SO}$ is a Malcev algebra and have recalculated known relations for the structure constants in terms of the introduced structure tensor. An application of the split Lie $3-$algebra to a Bagger and Lambert gauge theory is also discussed.
Quiver Gauge theories from Lie Superalgebras
Belhaj, A
2012-01-01
We discuss quiver gauge models with matter fields based on Dynkin diagrams of Lie superalgebra structures. We focus on A(1,0) case and we find first that it can be related to intersecting complex cycles with genus $g$. Using toric geometry, A(1,0) quivers are analyzed in some details and it is shown that A(1,0) can be used to incorporate fundamental fields to a product of two unitary factor groups. We expect that this approach can be applied to other kinds of Lie superalgebras;
Spiders for rank 2 Lie algebras
Kuperberg, G
1996-01-01
A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. We define certain combinatorial spiders by generators and relations that are isomorphic to the representation theories of the three rank two simple Lie algebras, namely A2, B2, and G2. They generalize the widely-used Temperley-Lieb spider for A1. Among other things, they yield bases for invariant spaces which are probably related to Lusztig's canonical bases, and they are useful for computing quantities such as generalized 6j-symbols and quantum link invariants.
Lie algebra contractions and separation of variables
Vinternits, P; Pogosyan, G S; Sissakian, A N
2001-01-01
The concept of analytical Lie group contractions is introduced to relate the separation of variables in space of constant nonzero curvature to separation in Euclidean or pseudo-Euclidean spaces. The contraction parameter is introduced explicitly into the basis of the Lie algebra, the Laplace-Beltrami operator, the complete set of commuting operators, the coordinates themselves and into the solutions. This enables to obtain asymptotic formulae connecting special functions related to the groups O(n) and O(n,1) to those related to Euclidean and pseudo-Euclidean groups
Lie Point Symmetries of Differential-Difference Equations
DING Wei; TANG Xiao-Yan
2004-01-01
In this paper, the classical Lie group approach is extended to find some Lie point symmetries of differentialdifference equations. It reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra.
Generalized double extension and descriptions of qadratic Lie superalgebras
Bajo, I; Bordemann, M
2007-01-01
A Lie superalgebra endowed with a supersymmetric, even, non-degenerate, invariant bilinear form is called a quadratic Lie superalgebra. In this paper we give inductive descriptions of quadratic Lie superalgebras in terms of generalized double extensions.
The Lie Algebras in which Every Subspace s Its Subalgebra
WU MING-ZHONG
2009-01-01
In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g+Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.
Lie, truth, lie: the role of task switching in a deception context.
Debey, Evelyne; Liefooghe, Baptist; De Houwer, Jan; Verschuere, Bruno
2015-05-01
A cornerstone of the task switching literature is the finding that task performance is typically slower and more error-prone when the task switches than when it repeats. So far, deception research has largely ignored that such cognitive switch costs should also emerge when switching between truth telling and lying, and may affect the cognitive cost of lying as reflected in higher prefrontal brain activity and slower and less accurate responding compared to truth telling. To get a grasp on the relative size of the switch costs associated with lying and truth telling, the current study had participants perform a reaction time-based deception task, in which they alternated between lying and telling the truth to yes/no questions that were related to activities performed in the lab (Experiment 1) or neutral autobiographical facts (Experiment 2). In both experiments, the error and reaction time switch costs were found to be equally large for switching from truth telling to lying and from lying to truth telling. This symmetry in switch costs can be explained from the hypothesis that lying requires a first step of truth telling, and demonstrates that task switching does not contribute to the cognitive cost of lying when the repetition/switch ratio is balanced. Theoretical and methodological implications are considered.
Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’
Eenkhoorn, P.; Graafland, J.J.
2010-01-01
The famous political philosopher Hannah Arendt develops several arguments why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt’s theory, we distinguish five reasons why lying is a structural tempt
Teaching the Truth about Lies to Psychology Students: The Speed Lying Task
Pearson, Matthew R.; Richardson, Thomas A.
2013-01-01
To teach the importance of deception in everyday social life, an in-class activity called the "Speed Lying Task" was given in an introductory social psychology class. In class, two major research findings were replicated: Individuals detected deception at levels no better than expected by chance and lie detection confidence was unrelated…
Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’
Eenkhoorn, P.; Graafland, J.J.
2010-01-01
The famous political philosopher Hannah Arendt develops several arguments why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt’s theory, we distinguish five reasons why lying is a structural tempt
Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’
Eenkhoorn, P.; Graafland, J.J.
2010-01-01
The famous political philosopher Hannah Arendt develops several arguments why truthfulness cannot be counted among the political virtues. This article shows that similar arguments apply to lying in business. Based on Hannah Arendt’s theory, we distinguish five reasons why lying is a structural
Teaching the Truth about Lies to Psychology Students: The Speed Lying Task
Pearson, Matthew R.; Richardson, Thomas A.
2013-01-01
To teach the importance of deception in everyday social life, an in-class activity called the "Speed Lying Task" was given in an introductory social psychology class. In class, two major research findings were replicated: Individuals detected deception at levels no better than expected by chance and lie detection confidence was unrelated…
Why Do Lie-Catchers Fail? A Lens Model Meta-Analysis of Human Lie Judgments
Hartwig, Maria; Bond, Charles F., Jr.
2011-01-01
Decades of research has shown that people are poor at detecting lies. Two explanations for this finding have been proposed. First, it has been suggested that lie detection is inaccurate because people rely on invalid cues when judging deception. Second, it has been suggested that lack of valid cues to deception limits accuracy. A series of 4…
Hiding an Inconvenient Truth : Lies and Vagueness
Serra Garcia, M.; van Damme, E.E.C.; Potters, J.J.M.
2010-01-01
When truth conflicts with e¢ ciency, can verbal communication destroy efficiency? Or are lies or vagueness used to hide inconvenient truths? We consider a sequential 2-player public good game in which the leader has private information about the value of the public good. This value can be low, high,
Are 'Lying Compositions' Detrimental To Student Growth?
2010-01-01
@@ A greater number of primary school students are inventing stories and telling lies when they are supposed to be writing about personal experiences. The Chengdu Business Daily said, of 40 pupils in a grade-four class, 30 wrote about how they struggled with human traffickers or thieves, and 26 pupils admitted they made the stories up.
Lie Algebra of Noncommutative Inhomogeneous Hopf Algebra
Lagraa, M
1997-01-01
We construct the vector space dual to the space of right-invariant differential forms construct from a first order differential calculus on inhomogeneous quantum group. We show that this vector space is equipped with a structure of a Hopf algebra which closes on a noncommutative Lie algebra satisfying a Jacobi identity.
SAYD modules over Lie-Hopf algebras
Rangipour, B
2011-01-01
In this paper a general van Est type isomorphism is established. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and SAYD modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is found at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes- Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate...
Happiness lies somewhere in your brain
梅寒
2007-01-01
<正> When I was a kid,I defined happinessas being able to afford anything that was de-sired and thus I came up with the conclusionthat happiness lies in the possession of mon-ey.Time turned me tall and smart,also,able
On Split Lie Triple Systems II
Antonio J Calderón Martín; M Forero Piulestán
2010-04-01
In [4] it is studied that the structure of split Lie triple systems with a coherent 0-root space, that is, satisfying $[T_0,T_0,T]=0$ and $[T_0,T_,T_0]≠ 0$ for any nonzero root and where $T_0$ denotes the 0-root space and $T_$ the -root space, by showing that any of such triple systems with a symmetric root system is of the form $T=\\mathcal{U}+\\sum_j I_j$ with $\\mathcal{U}$ a subspace of the 0-root space $T_0$ and any $I_j$ a well described ideal of , satisfying $[I_j,T,I_k]=0$ if $j≠ k$. It is also shown in [4] that under certain conditions, a split Lie triple system with a coherent 0-root space is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity of is characterized. In the present paper we extend these results to arbitrary split Lie triple systems with no restrictions on their 0-root spaces.
SAYD Modules over Lie-Hopf Algebras
Rangipour, Bahram; Sütlü, Serkan
2012-11-01
In this paper a general van Est type isomorphism is proved. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and those modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is proved at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes-Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate the whole theory on this example. Finally explicit representative cocycles of the cohomology classes for this example are calculated.
Nonlinear analysis of flexible plates lying on elastic foundation
Trushin Sergey
2017-01-01
Full Text Available This article describes numerical procedures for analysis of flexible rectangular plates lying on elastic foundation. Computing models are based on the theory of plates with account of transverse shear deformations. The finite difference energy method of discretization is used for reducing the initial continuum problem to finite dimensional problem. Solution procedures for nonlinear problem are based on Newton-Raphson method. This theory of plates and numerical methods have been used for investigation of nonlinear behavior of flexible plates on elastic foundation with different properties.
Recursion relations and branching rules for simple Lie algebras
Lyakhovsky, V D
1995-01-01
The branching rules between simple Lie algebras and its regular (maximal) simple subalgebras are studied. Two types of recursion relations for anomalous relative multiplicities are obtained. One of them is proved to be the factorized version of the other. The factorization property is based on the existence of the set of weights \\Gamma specific for each injection. The structure of \\Gamma is easily deduced from the correspondence between the root systems of algebra and subalgebra. The recursion relations thus obtained give rise to simple and effective algorithm for branching rules. The details are exposed by performing the explicit decomposition procedure for A_{3} \\oplus u(1) \\rightarrow B_{4} injection.
Techniques for searching first integrals by Lie group and application to gyroscope system
HU Yanxia; GUAN Keying
2005-01-01
In the paper, the methods of finding first integrals of an autonomous system using one-parameter Lie groups are discussed. A class of nontrivial one-parameter Lie groups admitted by the classical gyroscope system is found, and based on the properties of first integral determined by the one-parameter Lie group, the fourth first integral of the gyroscope system in Euler case, Lagrange case and Kovalevskaya case can be obtained in a uniform idea. An error on the fourth first integral in general Kovalevskaya case (A=B=2C,zG=0), which appeared in literature is found and corrected.
Infinite-Dimensional Lie Superalgebras SHO' over a Field of Prime Characteristic
HE Ying-hua; YANG Xi-geng; LI Yu-xia
2008-01-01
The natural filtrations of the infinite-dimensional modular Lie superalgebra SHO' are proved to be invariant under automorphisms of SHO'. The proof involves the investigation of the ad-nilpotent elements of the even part, and the determination of the subalgebras generated by certain ad-nilpotent elements. A property of automorphisms of these Lie superalgebras can be established, and an intrinsic characterization of SHO' can be obtained.
Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation
Rui, Wenjuan; Zhang, Xiangzhi
2016-05-01
This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.
Dimension of the $c$-nilpotent multiplier of Lie algebras
MEHDI ARASKHAN; MOHAMMAD REZA RISMANCHIAN
2016-08-01
The purpose of this paper is to derive some inequalities for dimension of the $c$-nilpotent multiplier of finite dimensional Lie algebras and their factor Lie algebras. We further obtain an inequality between dimensions of $c$-nilpotent multiplier of Lie algebra $L$ and tensor product of a central ideal by its abelianized factor Lie algebra
Legitimate lies : The relationship between omission, commission, and cheating
Pittarello, Andrea; Rubaltelli, Enrico; Motro, Daphna
2016-01-01
Across four experiments, we show that when people can serve their self-interest, they are more likely to refrain from reporting the truth ( lie of omission) than actively lie ( lie of commission). We developed a novel online "Heads or Tails" task in which participants can lie to win a monetary prize
Whittaker categories and strongly typical Whittaker modules for Lie superalgebras
Bagci, Irfan; Wiesner, Emilie
2012-01-01
Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra according to the action of an appropriate sub-superalgebra; and, for basic classical Lie superalgebras of type I, a description of the strongly typical simple Whittaker modules.
A Local Characterization of Lie Homomorphisms of Nest Algebras
YANG Miao-xia; ZHANG Jian-hua
2014-01-01
In this paper, linear maps preserving Lie products at zero points on nest algebras are studied. It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism. As an application, the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained.
Lie symmetries for equations in conformal geometries
Hansraj, S; Msomi, A M; Govinder, K S
2005-01-01
We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been found in practice. We use the method of Lie analysis of differential equations to obtain new group invariant solutions to conformally related Petrov type D spacetimes. Four cases arise depending on the nature of the Lie symmetry generator. In three cases we are in a position to solve the master field equation in terms of elementary functions. In the fourth case special solutions in terms of Bessel functions are obtained. These solutions contain known models as special cases.
Geodesic models generated by Lie symmetries
Abebe, G Z; Govinder, K S
2014-01-01
We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators that leave the junction condition invariant are identified and the optimal system is generated. We use each element of the optimal system to transform the partial differential equation to an ordinary differential equation. New exact solutions, which are group invariant under the action of Lie point infinitesimal symmetries, are found. We obtain families of traveling wave solutions and self-similar solutions, amongst others. The gravitational potentials are given in terms of elementary functions, and the line elements can be given explicitly in all cases. We show that the Friedmann dust model is regained as a special case, and we can connect our results to earlier investigations.
Analytic factorization of Lie group representations
Gimperlein, Heiko; Krötz, Bernhard; Lienau, Christoph
2012-01-01
For every moderate growth representation (p,E)(p,E) of a real Lie group G on a Fréchet space, we prove a factorization theorem of Dixmier–Malliavin type for the space of analytic vectors E¿E¿. There exists a natural algebra of superexponentially decreasing analytic functions A(G)A(G), such that E......¿=¿(A(G))E¿E¿=¿(A(G))E¿. As a corollary we obtain that E¿E¿ coincides with the space of analytic vectors for the Laplace–Beltrami operator on G.......For every moderate growth representation (p,E)(p,E) of a real Lie group G on a Fréchet space, we prove a factorization theorem of Dixmier–Malliavin type for the space of analytic vectors E¿E¿. There exists a natural algebra of superexponentially decreasing analytic functions A(G)A(G), such that E...
Harmonic analysis on exponential solvable Lie groups
Fujiwara, Hidenori
2015-01-01
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated alge...
Constructions of Lie algebras and their modules
Seligman, George B
1988-01-01
This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. T...
k-symplectic formalism on Lie algebroids
De Leon, M; De Diego, D Martin [Instituto de Ciencias Matematicas (CSIC-UAM-UC3M-UCM) C/Serrano 123, 28006 Madrid (Spain); Salgado, M; Vilarino, S [Departamento de XeometrIa e TopoloxIa, Facultade de Matematicas, Universidade de Santiago de Compostela, 15782-Santiago de Compostela (Spain)], E-mail: mdeleon@imaff.cfmac.csic.es, E-mail: d.martin@imaff.cfmac.csic.es, E-mail: modesto.salgado@usc.es, E-mail: silvia.vilarino@usc.es
2009-09-25
In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of k-symplectic geometry. We discuss the relation between the Lagrangian and Hamiltonian descriptions through a convenient notion of Legendre transformation. The theory is a natural generalization of the standard one; in addition, other interesting examples are studied, in particular, systems with symmetry and Poisson-sigma models.
De Veaux, Richard D.; Hand, David J.
2005-01-01
As Huff’s landmark book made clear, lying with statistics can be accomplished in many ways. Distorting graphics, manipulating data or using biased samples are just a few of the tried and true methods. Failing to use the correct statistical procedure or failing to check the conditions for when the selected method is appropriate can distort results as well, whether the motives of the analyst are honorable or not. Even when the statistical procedure and motives are correct, bad data can produce ...
Lies, Incentives and Self-confidence
Maggian, Valeria
2013-01-01
The present thesis is composed by three chapters, each of them making contributions to three distinct topics in behavioral Economics. The chapters can thus be read independently from each other. The first chapter concerns an experimental analysis which aim is to examine the development of social preferences with respect to age and how they are related with lying behavior of children. The second chapter investigates the role of reciprocity in exacerbating inefficient and opportunistic behavior...
Spherical functions on affine Lie groups
Etingof, P; Kirillov, A A; Pavel Etingof; Igor Frenkel; Alexander Kirillov Jr
1994-01-01
We show that the space of holomorphic functions of a fixed degree on an affine Lie group which take values in a finite-dimensional representation of this group and are equivariant with respect to (twisted) conjugacy coin- cides with the space of conformal blocks of the Wess-Zumino-Witten conformal field theory on an elliptic curve with punctures, or, equivalently,with the space of states of the Chern-Simons topological field theory in genus 1. This provides a group-theoretic realization of the Segal modular functor for elliptic curves. We also show that the the radial part of the second order Laplace operator on an affine Lie group acting in the space of equivariant functions coincides with the operator defining the Knizhnik-Zamolodchikov connection on conformal blocks on elliptic curves, and its eigenfunctions coincide with the correlation functions of conformal blocks. At the critical value of the degree (minus the dual Coxeter number of the underlying simple Lie algebra) there exist higher order Laplace op...
COMPLETE LIE ALGEBRAS WITH l-STEP NILPOTENT RADICALS
高永存; 孟道冀
2002-01-01
The authors first give a necessary and sufficient condition for some solvable Lie algebras with l-step nilpotent radicals to be complete, and then construct a new class of infinite dimensional complete Lie algebras by using the modules of simple Lie algebras. The quotient algebras of this new constructed Lie algebras are non-solvable complete Lie algebras with l-step nilpotent radicals.
Classification of filiform Lie algebras of order 3
Navarro, Rosa María
2016-12-01
Lie algebras of order 3 constitute a generalization of Lie algebras and superalgebras. Throughout this paper the classification problem of filiform Lie algebras of order 3 is considered and therefore this work is a continuation papers seen in the literature. We approach this classification by extending Vergne's result for filiform Lie algebras and by considering algebras of order 3 of high nilindex. We find the expression of the law to which any elementary filiform Lie algebra of order 3 is isomorphic.
Lie color 代数的商代数%Algebras of quotients of Lie color algebras
裴凤; 周建华
2004-01-01
介绍了Lie color 代数的一些性质,如素性、半素性、非退化性等.给出了Lie color 代数的商代数以及弱商代数的概念,并把Lie color 代数的素性和半素性推广到它的商代数上.利用没有非零零化子的理想对Lie color 代数的商代数进行刻画,证明了:若L是Lie color 代数Q的子代数,则Q是L的商代数当且仅当Q理想吸收于L.通过具体构造证明了每一个半素Lie color 代数都有极大商代数,并给出这个极大商代数的等价刻画.
Engel's Theorem of Jordan Lie Algebra and Its Applications%Jordan李代数的Engel定理及其应用
钱玲; 周佳; 陈良云
2012-01-01
证明了有限维Jordan李代数的Engel定理,并应用它得到了Jordan李代数的Cartan子代数的若干性质.%The authors prove Engel's theorem of Jordan Lie algebra and apply it to get some properties of Cartan subalgebras on Jordan Lie algebra.
Abedi-Fardad, J.; Rezaei-Aghdam, A.; Haghighatdoost, Gh.
2017-01-01
We classify all four-dimensional real Lie bialgebras of symplectic type and obtain the classical r-matrices for these Lie bialgebras and Poisson structures on all the associated four-dimensional Poisson-Lie groups. We obtain some new integrable models where a Poisson-Lie group plays the role of the phase space and its dual Lie group plays the role of the symmetry group of the system.
Some quantum Lie algebras of type D{sub n} positive
Bautista, Cesar [Facultad de Ciencias de la Computacion, Benemerita Universidad Autonoma de Puebla, Edif 135, 14 sur y Av San Claudio, Ciudad Universitaria, Puebla Pue. CP 72570 (Mexico); Juarez-Ramirez, Maria Araceli [Facultad de Ciencias Fisico-Matematicas, Benemerita Universidad Autonoma de Puebla, Edif 158 Av San Claudio y Rio Verde sn Ciudad Universitaria, Puebla Pue. CP 72570 (Mexico)
2003-03-07
A quantum Lie algebra is constructed within the positive part of the Drinfeld-Jimbo quantum group of type D{sub n}. Our quantum Lie algebra structure includes a generalized antisymmetry property and a generalized Jacobi identity closely related to the braid equation. A generalized universal enveloping algebra of our quantum Lie algebra of type D{sub n} positive is proved to be the Drinfeld-Jimbo quantum group of the same type. The existence of such a generalized Lie algebra is reduced to an integer programming problem. Moreover, when the integer programming problem is feasible we show, by means of the generalized Jacobi identity, that the Poincare-Birkhoff-Witt theorem (basis) is still true.
Almost-Riemannian Geometry on Lie Groups
Ayala, Victor; Jouan, Philippe
2015-01-01
A simple Almost-Riemmanian Structure on a Lie group G is defined by a linear vector field and dim(G)-1 left-invariant ones. We state results about the singular locus, the abnormal extremals and the desingularization of such ARS's, and these results are illustrated by examples on the 2D affine and the Heisenberg groups.These ARS's are extended in two ways to homogeneous spaces, and a necessary and sufficient condition for an ARS on a manifold to be equivalent to a general ARS on a homogeneous ...
The graded Lie algebra of general relativity
Reiterer, Michael
2014-01-01
We construct a graded Lie algebra in which a solution to the vacuum Einstein equations is any element of degree 1 whose bracket with itself is zero. Each solution generates a cochain complex, whose first cohomology is linearized gravity about that solution. We gauge-fix to get a smaller cochain complex with the same cohomologies (deformation retraction). The new complex is much smaller, it consists of the solution spaces of linear homogeneous wave equations (symmetric hyperbolic equations). The algorithm that produces these gauges and wave equations is both for linearized gravity and the full Einstein equations. The gauge groupoid is the groupoid of rank 2 complex vector bundles.
The Technologies of Lie in Local Cultures of Western Siberia
Evgeny A. Naumenko
2016-12-01
Full Text Available The article is devoted to the political phenomenon – "technology of lie" that emerged of Jesuit and quasi-Catholic culture of Europe at the Middle Ages. The article also considers penetration of this phenomenon into Western Siberia through representatives of exile. According to author, the technologies of lie were created as a result of distortion of Catholicism, departure from a true spiritual component. This policy was considered by its carriers as a competition form. The author considers that misstatement of Orthodoxy was possible to a lesser extent because of its traditional dogmatism; the Russian imperial power did not use technologies of lie at the wide nation-wide and geopolitical level. The phenomenon existed only in local cultures. In article the social and economic and political reasons of forming of these technologies in the Russian Empire and Western Siberia, their manifestations and a consequence are analyzed. As examples cases of anti-Semitic "bloody slanders" are given in the European Russia and a defiant line item of the Jesuit organization in a Siberian exile. The author notes that the considered tactics has been directed to some religious groups and to certain representatives of society and the government. As a rule, none of the victims were ready to "information attacks" and lost them, losing not only property and positions, but also life sometimes. The author emphasizes that this practice has been adopted by part of the Russian revolutionary atheists. There is approved action of these technologies in terms of the Siberian penal servitude and the exile. Later the experience gained by them has formed the basis of fabricated political processes in case of the Stalin the regime.
Fermionic realisations of simple Lie algebras
de Azcárraga, J A
2000-01-01
We study the representation ${\\cal D}$ of a simple compact Lie algebra $\\g$ of rank l constructed with the aid of the hermitian Dirac matrices of a (${\\rm dim} \\g$)-dimensional euclidean space. The irreducible representations of $\\g$ contained in ${\\cal D}$ are found by providing a general construction on suitable fermionic Fock spaces. We give full details not only for the simplest odd and even cases, namely su(2) and su(3), but also for the next (${dim} \\g$)-even case of su(5). Our results are far reaching: they apply to any $\\g$-invariant quantum mechanical system containing ${\\rm dim} \\g$ fermions. Another reason for undertaking this study is to examine the role of the $\\g$-invariant fermionic operators that naturally arise. These are given in terms of products of an odd number of gamma matrices, and include, besides a cubic operator, (l-1) fermionic scalars of higher order. The latter are constructed from the Lie algebra cohomology cocycles, and must be considered to be of theoretical significance simila...
Koszul information geometry and Souriau Lie group thermodynamics
Barbaresco, Frédéric, E-mail: frederic.barbaresco@thalesgroup.com
2015-01-13
The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from 'Characteristic Functions', was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau in Statistical Physics. The Koszul-Vinberg Characteristic Function (KVCF) on convex cones will be presented as cornerstone of 'Information Geometry' theory, defining Koszul Entropy as Legendre transform of minus the logarithm of KVCF, and Fisher Information Metrics as hessian of these dual functions, invariant by their automorphisms. In parallel, Souriau has extended the Characteristic Function in Statistical Physics looking for other kinds of invariances through co-adjoint action of a group on its momentum space, defining physical observables like energy, heat and momentum as pure geometrical objects. In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck) Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. Fisher Information metric appears as the opposite of the derivative of Mean 'Moment map' by geometric temperature, equivalent to a Geometric Capacity or Specific Heat. These elements has been developed by author in [10][11].
Classical mechanics on noncommutative space with Lie-algebraic structure
Miao, Yan-Gang; Wang, Xu-Dong; Yu, Shao-Jie
2011-08-01
We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained in general due to some algebraic properties, such as the antisymmetry and Jacobi identity. Through solving the constraint equations the structure constants satisfy, we obtain two new sorts of algebraic structures, each of which corresponds to one type of noncommutative spaces. Based on such types of noncommutative spaces as the starting point, we analyze the classical motion of the particle interacting with a constant external force by means of the Hamiltonian formalism on a Poisson manifold. Our results not only include that of a recent work as our special cases, but also provide new trajectories of motion governed mainly by marvelous extra forces. The extra forces with the unimaginable tx˙-,(xx)˙-, and (xx)¨-dependence besides with the usual t-, x-, and x˙-dependence, originating from a variety of noncommutativity between different spatial coordinates and between spatial coordinates and momenta as well, deform greatly the particle's ordinary trajectories we are quite familiar with on the Euclidean (commutative) space.
BKM Lie superalgebras from counting twisted CHL dyons
Govindarajan, Suresh
2011-05-01
Following Sen, we study the counting of (`twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with mathcal{N} = 4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, are given in terms of multiplicative eta products with the Mathieu group, M 24, playing an important role. These multiplicative eta products enable us to construct Siegel modular forms that count twisted quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a special class of Siegel modular forms, the dd-modular forms, that have been classified by Clery and Gritsenko. We show that each one of these dd-modular forms arise as the Weyl-Kac-Borcherds denominator formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the Weyl chamber are in one-to-one correspondence with the walls of marginal stability in the corresponding CHL model for twisted dyons as well as untwisted ones. This leads to a periodic table of BKM Lie superalgebras with properties that are consistent with physical expectations.
Langlois, Michel
2014-01-01
In order to generalize the relativistic notion of boost to the case of non inertial particles and to general relativity, we come back to the definition of Lie group of Lorentz matrices and its Lie algebra and we study how this group acts on the Minskowski space. We thus define the notion of tangent boost along a worldline. This notion very general notion gives a useful tool both in special relativity (for non inertial particles or/and for non rectilinear coordinates) and in general relativity. We also introduce a matrix of the Lie algebra which, together with the tangent boost, gives the whole dynamical description of the considered system (acceleration and Thomas rotation). After studying the properties of Lie algebra matrices and of their reduced forms, we show that the Lie group of special Lorentz matrices has four one-parameter subgroups. These tools lead us to introduce the Thomas rotation in a quite general way. At the end of the paper, we present some examples using these tools and we consider the case...
Uncertainty Principles on Two Step Nilpotent Lie Groups
S K Ray
2001-08-01
We extend an uncertainty principle due to Cowling and Price to two step nilpotent Lie groups, which generalizes a classical theorem of Hardy. We also prove an analogue of Heisenberg inequality on two step nilpotent Lie groups.
Pants on fire: the electrophysiological signature of telling a lie.
Pfister, Roland; Foerster, Anna; Kunde, Wilfried
2014-01-01
Even though electroencephalography has played a prominent role for lie detection via personally relevant information, the electrophysiological signature of active lying is still elusive. We addressed this signature with two experiments in which participants helped a virtual police officer to locate a knife. Crucially, before this response, they announced whether they would lie or tell the truth about the knife's location. This design allowed us to study the signature of lie-telling in the absence of rare and personally significant oddball stimuli that are typically used for lie detection via electrophysiological markers, especially the P300 component. Our results indicate that active lying attenuated P300 amplitudes as well as N200 amplitudes for such non-oddball stimuli. These results support accounts that stress the high cognitive demand of lie-telling, including the need to suppress the truthful response and to generate a lie.
Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free Representations
Ling CHEN
2011-01-01
We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras (or corresponding Hamiltonian operators) associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu's generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility.
Lie symmetries and differential galois groups of linear equations
Oudshoorn, W.R.; Put, M. van der
2002-01-01
For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In co
33 CFR 401.92 - Wintering and lying-up.
2010-07-01
... 33 Navigation and Navigable Waters 3 2010-07-01 2010-07-01 false Wintering and lying-up. 401.92... OF TRANSPORTATION SEAWAY REGULATIONS AND RULES Regulations General § 401.92 Wintering and lying-up. No vessel shall winter within the Seaway or lie-up within the Seaway during the navigation...
Lie Pseudogroups à la Cartan from a Modern Perspective
Yudilevich, O.
2016-01-01
In 1904-05, the mathematician Élie Cartan published two pioneer papers in which he introduced a structure theory for Lie pseudogroups. Lie pseudogroups are mathematical objects that appear in both differential geometry and in the theory of differential equations as local symmetries of geometric stru
Graded Lie Algebra Generating of Parastatistical Algebraic Relations
JING Si-Cong; YANG Wei-Min; LI Ping
2001-01-01
A new kind of graded Lie algebra (We call it Z2,2 graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable Bose subspace of the Z2,2 graded Lie algebra and using relevant generalized Jacobi identities, we generate the whole algebraic structure of parastatistics.
Extremal projectors for contragredient Lie (super)symmetries (short review)
Tolstoy, V N
2010-01-01
A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody algebras and superalgebras, as well as their quantum $q$-analogs) is given. Some bibliographic comments on the applications of extremal projectors are presented.
Focal sampling of cow lying behaviour for automated welfare assessment
Mattachini, G.; Riva, E.; Bisaglia, C.; Pompe, J.C.A.M.; Provolo, G.
2013-01-01
the objective of the current study was to determine the number of focal animals required to represent the daily lying behaviour of a herd of lactating dairy cows. the study was carried out at 3 commercial dairy farms. the lying time (h/d) and number of lying bouts (n/d) of 15 ± 3 focal dairy cows,
Universal representations of Lie algebras by coderivations
Petracci, Emanuela
2003-01-01
A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincare'-Birkhoff-Witt theorem, extending this theorem to a class of nilpotent Lie superalgebras. Other applications are presented. Our results are new already for Lie algebras.
Lie symmetry algebra of one-dimensional nonconservative dynamical systems
Liu Cui-Mei; Wu Run-Heng; Fu Jing-Li
2007-01-01
Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping,the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.
Central Extension for the Triangular Derivation Lie Algebra
Chunming LI; Ping XU
2012-01-01
In this paper,we study a class of subalgebras of the Lie algebra of vector fields on n-dimensional torus,which are called the Triangular derivation Lie algebra.We give the structure and the central extension of Triangular derivation Lie algebra.
[Counter-acception or abort and lie].
Maruani, G
1979-09-01
In this very short but fiery and violent paper against abortion the author states that most women seeking abortion are actually lying to themselves, pretending they want something which, in reality, they do not want, i.e. an abortion. The laws regulating abortion in most countries are such that a woman is practically forbidden to make an independent decision, despite, or because of the number of counseling sessions and of meetings with doctors that she must go through. Radio, television, newspapers and magazines, friends and relatives, all contribute to make of abortion a run-of-the-mill operation, while it should be seen as scandal, and as the total negation of any maternal instinct.
Lie algebraic noncommuting structures from reparametrisation symmetry
Gangopadhyay, S
2007-01-01
We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our paper \\cite{sg}) that for some special choices of the reparametrisation parameter $\\epsilon$, one can obtain space-space noncommuting structures which are Lie-algebraic in form even in the case of the relativistic free particle. The connection of these structures with the existing models in the literature is also briefly discussed. Further, there exists some values of $\\epsilon$ for which the noncommutativity in the space-space sector can be made to vanish. As a matter of internal consistency of our approach, we also study the angular momentum algebra in details.
On Quantum Lie Nilpotency of Order 2
E. A. Kireeva
2016-01-01
Full Text Available The paper investigates the free algebras of varieties of associative algebras modulo identities of quantum Lie nilpotency of order 1 and 2. Let q be an invertible element of the ground field K (or of its extension. The element[x,y]q = xy-qyxof the free associative algebra is called a quantum commutator. We consider the algebras modulo identities [x,y]q = 0 (1and [[x,y]q ,z]q = 0. (2It is natural to consider the aforementioned algebras as the quantum analogs of commutative algebras and algebras of Lie nilpotency of order 2. The free algebras of the varieties of associative algebras modulo the identity of Lie nilpotency of order 2, that is the identity[[x,y] ,z] =0,where [x,y]=xy-yx is a Lie commutator, are of great interest in the theory of algebras with polynomial identities, since it was proved by A.V.Grishin for algebras over fields of characteristic 2, and V.V.Shchigolev for algebras over fields of characteristic p>2, that these algebras contain non-finitely generated T-spaces.We prove in the paper that the algebras modulo identities (1 and (2 are nilpotent in the usual sense and calculate precisely the nilpotency order of these algebras. More precisely, we prove that the free algebra of the variety of associative algebras modulo identity (1 is nilpotent of order 2 if q ≠ ± 1, and nilpotent of order 3 if q = - 1 and the characteristic of K is not equal to 2. It is also proved that the free algebra of the variety of associative algebras modulo identity (2 is nilpotent of order 3 if q3 ≠ 1, q ≠ ± 1, nilpotent of order 4 if q3 = 1, q ≠ 1, and nilpotent of
Detecting Children's Lies: Are Parents Accurate Judges of Their Own Children's Lies?
Talwar, Victoria; Renaud, Sarah-Jane; Conway, Lauryn
2015-01-01
The current study investigated whether parents are accurate judges of their own children's lie-telling behavior. Participants included 250 mother-child dyads. Children were between three and 11 years of age. A temptation resistance paradigm was used to elicit a minor transgressive behavior from the children involving peeking at a forbidden toy and…
Detecting Children's Lies: Are Parents Accurate Judges of Their Own Children's Lies?
Talwar, Victoria; Renaud, Sarah-Jane; Conway, Lauryn
2015-01-01
The current study investigated whether parents are accurate judges of their own children's lie-telling behavior. Participants included 250 mother-child dyads. Children were between three and 11 years of age. A temptation resistance paradigm was used to elicit a minor transgressive behavior from the children involving peeking at a forbidden toy and…
Field Theories on Canonical and Lie-Algebra Noncommutative Spacetimes
Amelino-Camelia, G; Doplicher, L; Amelino-Camelia, Giovanni; Arzano, Michele; Doplicher, Luisa
2002-01-01
Field theories on canonical noncommutative spacetimes, which are being studied also in connection with string theory, and on $\\kappa$-Minkowski spacetime, which is a popular example of Lie-algebra noncommutative spacetime, can be naturally constructed by introducing a suitable generating functional for Green functions in energy-momentum space. Direct reference to a star product is not necessary. It is sufficient to make use of the simple properties that the Fourier transform preserves in these spacetimes and establish the rules for products of wave exponentials that are dictated by the non-commutativity of the coordinates. The approach also provides an elementary description of "planar" and "non-planar" Feynman diagrams. We also comment on the rich phenomenology emerging from the analysis of these theories.
Field Theories on Canonical and Lie-Algebra Noncommutative Spacetimes
Amelino-Camelia, G.; Arzano, M.; Doplicher, L.
2003-01-01
Field theories on canonical noncommutative spacetimes, which are being studied also in connection with string theory, and on k-Minkowski spacetime, which is a popular example of Lie-algebra noncommutative spacetime, can be naturally constructed by introducing a suitable generating functional for Green functions in energy-momentum space. Direct reference to a star product is not necessary. It is sufficient to make use of the simple properties that the Fourier transform preserves in these spacetimes and establish the rules for products of wave exponentials that are dictated by the non-commutativity of the coordinates. The approach also provides an elementary description of "planar" and "non-planar" Feynman diagrams. We also comment on the rich phenomenology emerging from the analysis of these theories.
Automorphisms of Strong Homotopy Lie Algebras of Local Observables
Ritter, Patricia
2015-01-01
There is a well-established procedure of assigning a strong homotopy Lie algebra of local observables to a multisymplectic manifold which can be regarded as part of a categorified Poisson structure. For a 2-plectic manifold, the resulting Lie 2-algebra is isomorphic to a sub Lie 2-algebra of a natural Lie 2-algebra structure on an exact Courant algebroid. We generalize this statement to arbitrary n-plectic manifolds and study automorphisms on the arising Lie n-algebras. Our observations may be useful in studying the quantization problem on multisymplectic manifolds.
Determinantal formulae for the Casimir operators of inhomogeneous Lie algebras
Campoamor-Stursberg, Rutwig [Dpto. Geometria y Topologia, Fac CC Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias, 3, E-28040 Madrid (Spain)
2006-03-10
Contractions of Lie algebras are combined with the classical matrix method of Gel'fand to obtain matrix formulae for the Casimir operators of inhomogeneous Lie algebras. The method is presented for the inhomogeneous pseudo-unitary Lie algebras Iu(p,q). This procedure is extended to contractions of Iu(p,q) isomorphic to an extension by a derivation of the inhomogeneous special pseudo-unitary Lie algebras Isu(p-1,q), providing an additional analytical method to obtain their invariants. Further, matrix formulae for the invariants of other inhomogeneous Lie algebras are presented.
Pro-Lie Groups: A Survey with Open Problems
Karl H. Hofmann
2015-07-01
Full Text Available A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete category. It includes each finite-dimensional Lie group, each locally-compact group that has a compact quotient group modulo its identity component and, thus, in particular, each compact and each connected locally-compact group; it also includes all locally-compact Abelian groups. This paper provides an overview of the structure theory and the Lie theory of pro-Lie groups, including results more recent than those in the authors’ reference book on pro-Lie groups. Significantly, it also includes a review of the recent insight that weakly-complete unital algebras provide a natural habitat for both pro-Lie algebras and pro-Lie groups, indeed for the exponential function that links the two. (A topological vector space is weakly complete if it is isomorphic to a power RX of an arbitrary set of copies of R. This class of real vector spaces is at the basis of the Lie theory of pro-Lie groups. The article also lists 12 open questions connected to pro-Lie groups.
Lie symmetry analysis and soliton solutions of time-fractional $K(m, n)$ equation
G W WANG; M S HASHEMI
2017-01-01
In this note, method of Lie symmetries is applied to investigate symmetry properties of timefractional $K(m, n)$ equation with the Riemann–Liouville derivatives. Reduction of time-fractional $K(m, n)$ equation is done by virtue of the Erdélyi–Kober fractional derivative which depends on a parameter α. Thensoliton solutions are extracted by means of a transformation.
Moving Picture, Lying Image: Unreliable Cinematic Narratives
Csönge Tamás
2015-08-01
Full Text Available By coining the term “unreliable narrator” Wayne Booth hypothesized another agent in his model besides the author, the implicit author, to explain the double coding of narratives where a distorted view of reality and the exposure of this distortion are presented simultaneously. The article deals with the applicability of the concept in visual narratives. Since unreliability is traditionally considered to be intertwined with first person narratives, it works through subjective mediators. According to scholarly literature on the subject, the narrator has to be strongly characterized, or in other words, anthropomorphized. In the case of film, the main problem is that the narrator is either missing or the narration cannot be attributed entirely to them. There is a medial rupture where the apparatus mediates the story instead of a character’s oral or written discourse. The present paper focuses on some important but overlooked questions about the nature of cinematic storytelling through a re-examination of |the lying flashback in Alfred Hitchcock's Stage Fright. Can a character-narrator control the images the viewer sees? How can the filmic image still be unreliable without having an anthropomorphic narrator? How useful is the term focalization when we are dealing with embedded character-narratives in film?
Polytope expansion of Lie characters and applications
Walton, Mark A., E-mail: walton@uleth.ca [Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada)
2013-12-15
The weight systems of finite-dimensional representations of complex, simple Lie algebras exhibit patterns beyond Weyl-group symmetry. These patterns occur because weight systems can be decomposed into lattice polytopes in a natural way. Since lattice polytopes are relatively simple, this decomposition is useful, in addition to being more economical than the decomposition into single weights. An expansion of characters into polytope sums follows from the polytope decomposition of weight systems. We study this polytope expansion here. A new, general formula is given for the polytope sums involved. The combinatorics of the polytope expansion are analyzed; we point out that they are reduced from those of the Weyl character formula (described by the Kostant partition function) in an optimal way. We also show that the weight multiplicities can be found easily from the polytope multiplicities, indicating explicitly the equivalence of the two descriptions. Finally, we demonstrate the utility of the polytope expansion by showing how polytope multiplicities can be used in the calculation of tensor product decompositions, and subalgebra branching rules.
Devious Lies: Adventures in Freelance Science Outreach
Fatland, D. R.
2003-12-01
Observations are given from two freelance science outreach projects undertaken by the author: Tutoring at-risk secondary students and teaching astronomy to 5th-7th graders in a camp retreat environment. Two recurring thematic challenges in these experiences are considered: First the 'Misperception Problem', the institutionalized chasm between the process of doing science and K-12 science education (wherein science is often portrayed as something distant and inaccessible, while ironically children are necessarily excellent scientists). And second the 'Engagement Problem', engaging a student's attention and energy by matching teaching material and--more importantly--teaching techniques to the student's state of development. The objective of this work is twofold: To learn how to address these two challenges and to empower the students in a manner independent of the scientific content of any particular subject. An underlying hypothesis is that confidence to problem solve (a desirable life-skill) can be made more accessible through a combination of problem solving by the student and seeing how others have solved seemingly impossible problems. This hypothesis (or agenda) compels an emphasis on critical thinking and raises the dilemma of reconciling non-directed teaching with very pointed conclusions about the verity of pseudo-science and ideas prevalent about science in popular culture. An interesting pedagogical found-object in this regard is the useful 'devious lie' which can encourage a student to question the assumption that the teacher (and by extension any professed expert) has the right answers.
Relativity symmetries and Lie algebra contractions
Cho, Dai-Ning; Kong, Otto C.W., E-mail: otto@phy.ncu.edu.tw
2014-12-15
We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m,n) symmetry as an isometry on an m+n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension m+n−1, e.g. a G(m,n−1), together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4), which is the particular case for our interest on the physics side as the proposed relativity symmetry for “quantum spacetime”. The contractions from G(1,3) may be relevant to real physics.
Morales, A. I.; Benzoni, G.; Watanabe, H.; Nishimura, S.; Browne, F.; Daido, R.; Doornenbal, P.; Fang, Y.; Lorusso, G.; Patel, Z.; Rice, S.; Sinclair, L.; Söderström, P.-A.; Sumikama, T.; Wu, J.; Xu, Z. Y.; Yagi, A.; Yokoyama, R.; Baba, H.; Avigo, R.; Bello Garrote, F. L.; Blasi, N.; Bracco, A.; Camera, F.; Ceruti, S.; Crespi, F. C. L.; de Angelis, G.; Delattre, M.-C.; Dombradi, Zs.; Gottardo, A.; Isobe, T.; Kojouharov, I.; Kurz, N.; Kuti, I.; Matsui, K.; Melon, B.; Mengoni, D.; Miyazaki, T.; Modamio-Hoyborg, V.; Momiyama, S.; Napoli, D. R.; Niikura, M.; Orlandi, R.; Sakurai, H.; Sahin, E.; Sohler, D.; Shaffner, H.; Taniuchi, R.; Taprogge, J.; Vajta, Zs.; Valiente-Dobón, J. J.; Wieland, O.; Yalcinkaya, M.
2016-03-01
Low-lying excited states in 72Ni have been investigated in an in-flight fission experiment at the RIBF facility of the RIKEN Nishina Center. The combination of the state-of-the-art BigRIPS and EURICA setups has allowed for a very accurate study of the β decay from 72Co to 72Ni, and has provided first experimental information on the decay sequence 72Fe→72Co→72Ni and on the delayed neutron-emission branch 73Co→72Ni . Accordingly, we report nearly 60 previously unobserved γ transitions which deexcite 21 new levels in 72Ni. Evidence for the location of the so-sought-after (42+) ,(62+) , and (81+) seniority states is provided. As well, the existence of a low-spin β -decaying isomer in odd-odd neutron-rich Co isotopes is confirmed for mass A =72 . The new experimental information is compared to simple shell-model calculations including only neutron excitations across the f p g shells. It is shown that, in general, the calculations reproduce well the observed states.
Lie group classification and exact solutions of the generalized Kompaneets equations
Oleksii Patsiuk
2015-04-01
Full Text Available We study generalized Kompaneets equations (GKEs with one functional parameter, and using the Lie-Ovsiannikov algorithm, we carried out the group classification. It is shown that the kernel algebra of the full groups of the GKEs is the one-dimensional Lie algebra. Using the direct method, we find the equivalence group. We obtain six non-equivalent (up to transformations from the equivalence group GKEs that allow wider invariance algebras than the kernel one. We find a number of exact solutions of the non-linear GKE which has the maximal symmetry properties.
Multicomponent Group-Related Coherent States for Lie Group Chain G K
HE Hui-Yong; LI Guang-Hua; LI Jiang-Fan
2001-01-01
The multicomponent group-related coherent states for the Lie group chain G K are introduced. Their coupling coefficients are presented. The relations between these coupling coefficients and those (in the usual sense) of the irreducible representation bases labelled by G K are obtained. The generalized Racah's factorization lemma about the coupling coefficients of such coherent states is given. As an example, the multicomponent group-related coherent states for the Lie group chain Sp(4) D SO(3)1 S0(3)2 are found. The uncertainty relation and the squeezing property are discussed.``
Clustered Numerical Data Analysis Using Markov Lie Monoid Based Networks
Johnson, Joseph
2016-03-01
We have designed and build an optimal numerical standardization algorithm that links numerical values with their associated units, error level, and defining metadata thus supporting automated data exchange and new levels of artificial intelligence (AI). The software manages all dimensional and error analysis and computational tracing. Tables of entities verses properties of these generalized numbers (called ``metanumbers'') support a transformation of each table into a network among the entities and another network among their properties where the network connection matrix is based upon a proximity metric between the two items. We previously proved that every network is isomorphic to the Lie algebra that generates continuous Markov transformations. We have also shown that the eigenvectors of these Markov matrices provide an agnostic clustering of the underlying patterns. We will present this methodology and show how our new work on conversion of scientific numerical data through this process can reveal underlying information clusters ordered by the eigenvalues. We will also show how the linking of clusters from different tables can be used to form a ``supernet'' of all numerical information supporting new initiatives in AI.
Lie transforms and their use in Hamiltonian perturbation theory
Cary, J.R.
1978-06-01
A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here.
Electron delocalization and aromaticity in low-lying excited states of archetypal organic compounds.
Feixas, Ferran; Vandenbussche, Jelle; Bultinck, Patrick; Matito, Eduard; Solà, Miquel
2011-12-14
Aromaticity is a property usually linked to the ground state of stable molecules. Although it is well-known that certain excited states are unquestionably aromatic, the aromaticity of excited states remains rather unexplored. To move one step forward in the comprehension of aromaticity in excited states, in this work we analyze the electron delocalization and aromaticity of a series of low-lying excited states of cyclobutadiene, benzene, and cyclooctatetraene with different multiplicities at the CASSCF level by means of electron delocalization measures. While our results are in agreement with Baird's rule for the aromaticity of the lowest-lying triplet excited state in annulenes having 4nπ-electrons, they do not support Soncini and Fowler's generalization of Baird's rule pointing out that the lowest-lying quintet state of benzene and septet state of cyclooctatetraene are not aromatic.
Low-lying Photoexcited States of a One-Dimensional Ionic Extended Hubbard Model
Yokoi, Kota; Maeshima, Nobuya; Hino, Ken-ichi
2017-10-01
We investigate the properties of low-lying photoexcited states of a one-dimensional (1D) ionic extended Hubbard model at half-filling. Numerical analysis by using the full and Lanczos diagonalization methods shows that, in the ionic phase, there exist low-lying photoexcited states below the charge transfer gap. As a result of comparison with numerical data for the 1D antiferromagnetic (AF) Heisenberg model, it was found that, for a small alternating potential Δ, these low-lying photoexcited states are spin excitations, which is consistent with a previous analytical study [Katsura et al., Phys. Rev. Lett. 103, 177402 (2009)]. As Δ increases, the spectral intensity of the 1D ionic extended Hubbard model rapidly deviates from that of the 1D AF Heisenberg model and it is clarified that this deviation is due to the neutral-ionic domain wall, an elementary excitation near the neutral-ionic transition point.
Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System
FANG Jian-Hui; YAN Xiang-Hong; LI Hong; CHEN Pei-Sheng
2004-01-01
The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained.An example is given to illustrate the application of the result.
Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems
Wang Xing-Zhong; Fu Hao; Fu Jing-Li
2012-01-01
This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems.Firstly,the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action.Secondly,the determining equations and structure equation of Lie symmetry of the system are obtained.Thirdly,the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems.Finally,an example is discussed to illustrate the application of the results.
Magnetic pseudo-differential Weyl calculus on nilpotent Lie groups
Beltita, Ingrid
2009-01-01
We develop a pseudo-differential Weyl calculus on nilpotent Lie groups which allows one to deal with magnetic perturbations of right invariant vector fields. For this purpose we investigate an infinite-dimensional Lie group constructed as the semidirect product of a nilpotent Lie grup and an appropriate function space thereon. We single out an appropriate coadjoint orbit in the semidirect product and construct our pseudo-differential calculus as a Weyl quantization of that orbit.
Lie symmetries and invariants of constrained Hamiltonian systems
Liu Rong-Wan; Chen Li-Qun
2004-01-01
According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.
A new kind of graded Lie algebra and parastatistical supersymmetry
无
2001-01-01
In this paper the usual Z2 graded Lie algebra is generalized to a new form, which may be called Z2,2 graded Lie algebra. It is shown that there exist close connections between the Z2,2 graded Lie algebra and parastatistics, so the Z2,2 can be used to study and analyse various symmetries and supersymmetries of the paraparticle systems.
ON THE NOETHER SYMMETRY AND LIE SYMMETRY OF MECHANICAL SYSTEMS
梅凤翔; 郑改华
2002-01-01
The Noether symmetry is an invariance of Hamilton action under infinitesimal transformations of time and the coordinates. The Lie symmetry is an invariance of the differential equations of motion under the transformations. In this paper, the relation between these two symmetries is proved definitely and firstly for mechanical systems. The results indicate that all the Noether symmetries are Lie symmetries for Lagrangian systems meanwhile a Noether symmetry is a Lie symmetry for the general holonomic or nonholonomic systems provided that some conditions hold.
Construction of Lie algebras and invariant tensors through abelian semigroups
Izaurieta, Fernando; RodrIguez, Eduardo; Salgado, Patricio [Departamento de Fisica, Universidad de Concepcion, Casilla 160-C, Concepcion (Chile)], E-mail: fizaurie@gmail.com, E-mail: edurodriguez@udec.cl, E-mail: pasalgad@udec.cl
2008-11-01
The Abelian Semigroup Expansion Method for Lie Algebras is briefly explained. Given a Lie Algebra and a discrete abelian semigroup, the method allows us to directly build new Lie Algebras with their corresponding non-trivial invariant tensors. The Method is especially interesting in the context of M-Theory, because it allows us to construct M-Algebra Invariant Chern-Simons/Transgression Lagrangians in d = 11.
Noether-Lie Symmetry of Generalized Classical Mechanical Systems
JIA Wen-Zhi; ZHANG Xiao-Ni; WANG Shun-Jin; FANG Jian-Hui; WANG Peng; DING Ning
2008-01-01
In this paper, the Noether-Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether-Lie symmetry are obtained. An example is given to illustrate the application of the results.
The index of centralizers of elements of reductive Lie algebras
Charbonnel, Jean-Yves
2010-01-01
For a finite dimensional complex Lie algebra, its index is the minimal dimension of stabilizers for the coadjoint action. A famous conjecture due to Elashvili says that the index of the centralizer of an element of a reductive Lie algebra is equal to the rank. That conjecture caught attention of several Lie theorists for years. In this paper we give an almost general proof of that conjecture.
Flexible and fixed partitions in freestalls--effects on lying behavior and cow preference.
Ruud, L E; Bøe, K E
2011-10-01
The objective was to investigate the effect of stall partition design on total lying time, lying position, and stall cleanliness, and to evaluate the preferences of cows regarding stalls with traditional fixed stall dividers or flexible stall dividers. Using a crossover design, 16 nonlactating dairy cows were housed singly for 9 d in pens with 2 freestalls, 1 with fixed cantilever dividers and 1 with flexible dividers. The cows were first given access to one stall type, and then to the other type of stall, and finally to both in a preference test. Type of stall divider did not influence lying behavior (13.5h for fixed versus 14.0 h for flexible, ± 0.4h), lying positions, or stall cleanliness; however, the cows showed a preference for lying in the flexible stalls (65.2 for flexible vs. 34.8 for fixed ± 8.2%). This indicated that cows are able to distinguish between type of stall divider and that it is important to them; however, it is not clear if the reason for this is the shape or the properties of the dividers. We concluded that cattle chose a flexible stall divider over a fixed one, but the long-term consequences of this preference are not clear, because no obvious changes in stall usage were observed when cows were only given access to one type of divider. Copyright © 2011 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.
Boolean-Lie algebras and the Leibniz rule
Bazso, Fueloep [KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, PO Box 49, H-1525 Budapest (Hungary); Labos, Elemer [Neurobiology Research Group, United Research Organization of the Hungarian Academy of Sciences and Semmelweis University, H-1450 Budapest, PO Box 95 (Hungary)
2006-06-02
Using internal negations acting on Boolean functions, the notion of Boolean-Lie algebra is introduced. The underlying Lie product is the Boolean analogue of the Poisson bracket. The structure of a Boolean-Lie algebra is determined; it turns out to be solvable, but not nilpotent. We prove that the adjoint representation of an element of the Boolean-Lie algebra acts as a derivative operator on the space of Boolean functions. The adjoint representation is related to the previously known concept of the sensitivity function. Using the notion of adjoint representation we give the definition of a temporal derivative applicable to iterative dynamics of Boolean mappings.
The Lie algebra of infinitesimal symmetries of nonlinear diffusion equations
Kersten, Paul H.M.; Gragert, Peter K.H.
1983-01-01
By using developed software for solving overdetermined systems of partial differential equations, the authors establish the complete Lie algebra of infinitesimal symmetries of nonlinear diffusion equations.
The structure of split regular BiHom-Lie algebras
Calderón, Antonio J.; Sánchez, José M.
2016-12-01
We introduce the class of split regular BiHom-Lie algebras as the natural extension of the one of split Hom-Lie algebras and so of split Lie algebras. We show that an arbitrary split regular BiHom-Lie algebra L is of the form L = U +∑jIj with U a linear subspace of a fixed maximal abelian subalgebra H and any Ij a well described (split) ideal of L, satisfying [Ij ,Ik ] = 0 if j ≠ k. Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its simple ideals.
Construction of the elliptic Gaudin system based on Lie algebra
CAO Li-ke; LIANG Hong; PENG Dan-tao; YANG Tao; YUE Rui-hong
2007-01-01
Gaudin model is a very important integrable model in both quantum field theory and condensed matter physics.The integrability of Gaudin models is related to classical r-matrices of simple Lie algebras and semi-simple Lie algebra.Since most of the constructions of Gaudin models works concerned mainly on rational and trigonometric Gaudin algebras or just in a particular Lie algebra as an alternative to the matrix entry calculations often presented, in this paper we give our calculations in terms of a basis of the typical Lie algebra, An, Bn, Cn, Dn, and we calculate a classical r-matrix for the elliptic Gaudin system with spin.
On Integrable Roots in Split Lie Triple Systems
A.J.CALDER(O)N MART(I)N
2009-01-01
We focus on the notion of an integrable root in the framework of split Lie triple systems T with a coherent 0-root space. As a main result, it is shown that if T has all its nonzero roots integrable, then its standard embedding is a split Lie algebra having all its nonzero roots integrable. As a consequence, a local finiteness theorem for split Lie triple systems, saying that whenever all nonzero roots of T are integrable then T is locally finite, is stated. Finally, a classification theorem for split simple Lie triple systems having all its nonzero roots integrable is given.
Optimal Control Theory on almost-Lie Algebroids
Jozwikowski, Michal
2011-01-01
We extend the Pontryagin Maximum Principle (PMP) to the geometric setting of almost-Lie (AL) algebroids -- objects which generalize Lie algebroids. The result may be understood as a very general reduction scheme for optimal control problems (OCPs). It covers the standard PMP, as well as gives necessary optimality conditions for symmetric OCPs on Lie groups, principal bundles, and Lie groupoids. We do not assume the symmetry of boundary conditions. The ideas are based on a very general concept of homotopy of admissible paths on AL algebroids. Our framework works for OCPs with fixed-end-points and general boundary conditions.
3-Lie bialgebras (Lb,Cd and (Lb,Ce
Bai Ruipu
2016-05-01
Full Text Available Four dimensional $3$-Lie coalgebras with two-dimensional derived algebras, and four-dimensional $3$-Lie bialgebras of type $(L_b, C_c$ are classified. It is proved that there exist three classes of four dimensional $3$-Lie coalgebras with two-dimensional derived algebra which are $(L, C_{c_i}$, $i=1, 2, 3$ (Lemma 3.1, and ten classes of four dimensional $3$-Lie bialgebras of type $(L_b, C_c$ (Theorem 3.2.
What Lies Below a Martian Ice Cap
2008-01-01
for the north polar layered deposits. BU stands for basal unit, an ice-sand deposit that lies beneath parts of the north polar layered deposits. The Shallow Radar instrument was provided by the Italian Space Agency. Its operations are led by the University of Rome and its data are analyzed by a joint U.S.-Italian science team. JPL, a division of the California Institute of Technology, Pasadena, manages the Mars Reconnaissance Orbiter for the NASA Science Mission Directorate, Washington.
Frattini Subalgebras and Nonimbedding Theorem of n-Lie Algebras%n-Lie代数的Frattini子代数及非嵌入定理
白瑞蒲; 周和月; 刘学文
2006-01-01
In this paper, we prove the nonimbedding theorem in nilpotent n-Lie algebras which is an analogue to the nonimbedding theorem of Burnsids in groups of prime power order. We also study the properties of Frattini suialgebras of n-Lie algebras over the field with characteristic zero, and prove that the Frattini subalgebra of any k-solvable (k≥2) n-Lie algebra is zero.
Classical r-matrices of real low-dimensional Jacobi-Lie bialgebras and their Jacobi-Lie groups
Rezaei-Aghdam, A.; Sephid, M.
2014-01-01
In this research we obtain the classical r-matrices of real two and three dimensional Jacobi-Lie bialgebras. In this way, we classify all non-isomorphic real two and three dimensional coboundary Jacobi-Lie bialgebras and their types (triangular and quasitriangular). Also, we obtain the generalized Sklyanin bracket formula by use of which, we calculate the Jacobi structures on the related Jacobi-Lie groups. Finally, we present a new method for constructing classical integrable systems using co...
On the Correct Use of Statistical Tests: Reply to "Lies, damned lies and statistics (in Geology)"
Sornette, D
2010-01-01
In a recent Forum in EOS entitled "Lies, damned lies and statistics (in Geology)", Vermeesch (2009) claims that "statistical significant is not the same as geological significant", in other words, statistical tests may be misleading. In complete contradiction, we affirm that statistical tests are always informative. We trace the erroneous claim of Vermeesch (2009) to a mistake in the interpretation of the chi-square test. Furthermore, using the same catalog of 118,415 earthquakes of magnitude 4 or greater and occurring between Friday 1st January 1999 and Thursday, 1 January 2009 (USGS, http://earthquake.usgs.gov), we show that the null hypothesis that "the occurrence of earthquakes does not depend on the day of the week" cannot be rejected (p-value equal to p=0.46), when taking into account the two well-known effects of (i) catalog incompleteness and (ii) aftershock clustering. This corrects the p-value p=4.5 10^{-18} found by P. Vermeesch (2009), whose implementation of the chi-square test assumes that the 1...
Lie Algebroids in Classical Mechanics and Optimal Control
Eduardo Martínez
2007-03-01
Full Text Available We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie algebroids and we show how to reduce Pontryagin maximum principle.
Quantum Lie algebras of type A$_{n}$
Sudbery, A I
1995-01-01
It is shown that the quantised enveloping algebra of sl(n) contains a quantum Lie algebra, defined by means of axioms similar to Woronowicz's. This gives rise to Lie algebra-like generators and relations for the locally finite part of the quantised enveloping algebra, and suggests a canonical Poincare-Birkhoff-Witt basis.
Linear algebra meets Lie algebra: the Kostant-Wallach theory
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.
Structures of W(2.2 Lie conformal algebra
Yuan Lamei
2016-01-01
. In this paper, we study conformal derivations, central extensions and conformal modules for this Lie conformal algebra. Also, we compute the cohomology of this Lie conformal algebra with coefficients in its modules. In particular, we determine its cohomology with trivial coefficients both for the basic and reduced complexes.
Construction of Lie Superalgebras from Triple Product Systems
Okubo, Susumu
2003-01-01
Any simple Lie superalgebras over the complex field can be constructed from some triple systems. Examples of Lie superalgebras $D(2,1;\\alpha)$, G(3) and F(4) are given by utilizing a general construction method based upon $(-1,-1)$ balanced Freudenthal-Kantor triple system.
Lie Symmetry and Hojman Conserved Quantity of Maggi Equations
HU Chu-le; XIE Jia-fang
2007-01-01
Lie symmetry of Maggi equations is studied. Its determining equation and restriction equation of nonholonomic constraint are given. A Hojman conserved quantity can be deduced directly by using the Lie symmetry. An example is given to illustrate the application of the result.
Lying in Children's Fiction: Morality and the Imagination
Ringrose, Christopher
2006-01-01
The telling of lies is significant in fiction written for children, and is often (though not in all cases) performed by child protagonists. Lying can be examined from at least three perspectives: philosophical, moral and aesthetic. The moral and the aesthetic are the most significant for children's literature. Morality has been subtly dealt with…
Social and Cognitive Correlates of Children's Lying Behavior
Talwar, Victoria; Lee, Kang
2008-01-01
The relation between children's lie-telling and their social and cognitive development was examined. Children (3-8 years) were told not to peek at a toy. Most children peeked and later lied about peeking. Children's subsequent verbal statements were not always consistent with their initial denial and leaked critical information revealing their…
THE KILLING FORMS AND DECOMPOSITION THEOREMS OF LIE SUPERTRIPLE SYSTEMS
Zhang Zhixue; Jia Peipei
2009-01-01
In this article, the Killing form of a Lie supertriple system (LSTS) and that of its imbedding Lie superalgebra (LSA) are investigated, and a unique decomposition theorem for a quasiclassical LSTS with trivial center is established by means of the parallel decomposition theorem for a quasiclassical LSA.
The index of geometric operators on Lie Groupoids
Pflaum, M.J.; Posthuma, H.; Tang, X.
2014-01-01
We revisit the cohomological index theorem for elliptic elements in the universal enveloping algebra of a Lie groupoid previously proved by the authors. We prove a Thom isomorphism for Lie algebroids which enables us to rewrite the "topological side" of the index theorem. This results in index formu
Superderivations for a Family of Lie Superalgebras of Special Type*
SUN XIU-MEI; ZOU XU-JUAN; LIU WEN-DE
2011-01-01
By means of generators, superderivations are completely determined for a family of Lie superalgebras of special type, the tensor products of the exterior algebras and the finite-dimensional special Lie algebras over a field of characteristic p ＞ 3. In particular, the structure of the outer superderivation algebra is concretely formulated and the dimension of the first cohomology group is given.
Computations with reachable elements in simple Lie algebras
de Graaf, Willem
2010-01-01
We report on some computations with reachable elements in simple Lie algebras of exceptional type within the SLA package of GAP4. These computations confirm the classification of such elements by Elashvili and Grelaud. Secondly they answer a question from Panyushev. Thirdly they show in what way a recent result of Yakimova for the Lie algebras of classical type extends to the exceptional types.
Poisson-Lie T-Duality and Bianchi Type Algebras
Jafarizadeh, M A
1999-01-01
All Bianchi bialgebras have been obtained. By introducing a non-degenerate adjoint invariant inner product over these bialgebras the associated Drinfeld doubles have been constructed, then by calculating the coupling matrices for these bialgebras several \\sigma-models with Poisson-Lie symmetry have been obtained. Two simple examples as prototypes of Poisson-Lie dual models have been given.
Intrinsic characteristic classes for a local Lie group
Abadoglu, Ender
2009-01-01
For a local Lie group M we define odd order cohomology classes. The first class is an obstruction to globalizability of the local Lie group. The third class coincides with Godbillon-Vey class in a particular case. These classes are secondary as they emerge when curvature vanishes.
Linear algebra meets Lie algebra: the Kostant-Wallach theory
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.
On the simplicity of Lie algebras associated to Leavitt algebras
Abrams, Gene
2009-01-01
For any field $K$ and integer $n\\geq 2$ we consider the Leavitt algebra $L = L_K(n)$. $L$ is an associative algebra, but we view $L$ as a Lie algebra using the bracket $[a,b]=ab-ba$ for $a,b \\in L$. We denote this Lie algebra as $L^-$, and consider its Lie subalgebra $[L^-,L^-]$. In our main result, we show that $[L^-,L^-]$ is a simple Lie algebra if and only if char$(K)$ divides $n-1$. For any positive integer $d$ we let $S = M_d(L_K(n))$ be the $d\\times d$ matrix algebra over $L_K(n)$. We give sufficient conditions for the simplicity and non-simplicity of the Lie algebra $[S^-,S^-]$.
Non-filiform Characteristically Nilpotent and Complete Lie Algebras
José María Ancochea-Bermúdez; Rutwig Campoamor
2002-01-01
In this paper, we construct large families of characteristically nilpotent Lie algebras by considering deformations of the Lie algebra (g)4(m,m-1) of type Qn,which arises as a central naturally graded extension of the filiform Lie algebra Ln.By studying the graded cohomology spaces, we obtain that the sill algebras associated to the models (g)4(m,m-1) can be interpreted as nilradicals of solvable, complete Lie algebras. For extreme cocycles, we obtain moreover nilradicals of rigid laws.By considering supplementary cocycles, we construct, for any dimension n (＞－) 9,non-filiform characteristically nilpotent Lie algebras with mixed characteristic sequence and show that for certain deformations, these deformations are compatible with central extensions.
Authalic parameterization of general surfaces using Lie advection.
Zou, Guangyu; Hu, Jiaxi; Gu, Xianfeng; Hua, Jing
2011-12-01
Parameterization of complex surfaces constitutes a major means of visualizing highly convoluted geometric structures as well as other properties associated with the surface. It also enables users with the ability to navigate, orient, and focus on regions of interest within a global view and overcome the occlusions to inner concavities. In this paper, we propose a novel area-preserving surface parameterization method which is rigorous in theory, moderate in computation, yet easily extendable to surfaces of non-disc and closed-boundary topologies. Starting from the distortion induced by an initial parameterization, an area restoring diffeomorphic flow is constructed as a Lie advection of differential 2-forms along the manifold, which yields equality of the area elements between the domain and the original surface at its final state. Existence and uniqueness of result are assured through an analytical derivation. Based upon a triangulated surface representation, we also present an efficient algorithm in line with discrete differential modeling. As an exemplar application, the utilization of this method for the effective visualization of brain cortical imaging modalities is presented. Compared with conformal methods, our method can reveal more subtle surface patterns in a quantitative manner. It, therefore, provides a competitive alternative to the existing parameterization techniques for better surface-based analysis in various scenarios.
Test Rank of an Abelian Product of a Free Lie Algebra and a Free Abelian Lie Algebra
Naime Ekici; Nazar Şahin Öğüşlü
2011-08-01
Let be a free Lie algebra of rank ≥ 2 and be a free abelian Lie algebra of rank ≥ 2. We prove that the test rank of the abelian product $F× A$ is . Morever we compute the test rank of the algebra $F/ k(F)'$.
Lie symmetries of the shigesada-Kawasaki-Teramoto system
Cherniha, Roman; Davydovych, Vasyl'; Muzyka, Liliia
2017-04-01
The Shigesada-Kawasaki-Teramoto system, which consists of two reaction-diffusion equations with variable cross-diffusion and quadratic nonlinearities, is considered. The system is the most important case of the biologically motivated model proposed by Shigesada et al. (J. Theor. Biol.79(1979) 83-99). A complete description of Lie symmetries for this system is derived. It is proved that the Shigesada-Kawasaki-Teramoto system admits a wide range of different Lie symmetries depending on coefficient values. In particular, the Lie symmetry operators with highly unusual structure are unveiled and applied for finding exact solutions of the relevant nonlinear system with cross-diffusion.
Sophus Lie une pensée audacieuse
Stubhaug, Arild
2006-01-01
Sophus Lie (1842-1899) compte parmi les plus grandes figures norvgiennes de la science. La notorit que lui valent ses travaux n'a rien envier celle de son illustre compatriote Niels Henrik Abel. Groupes et alg bres de Lie ont acquis droit de cit dans maints domaines. Dans cette biographie dtaille, l'crivain Arild Stubhaug, puisant dans la volumineuse correspondance de Lie, dcrit l'homme et la socit norvgienne dans la seconde moiti du XIXe si cle. Le lecteur peut ainsi suivre son enfance dans un presbyt re nich au fond d'un fjord, dcouvrir les rformes de l'enseignement, voyager en Europe, frque
Graded Automorphism Group of TKK Lie Algebra over Semilattice
Zhang Sheng XIA
2011-01-01
Every extended affine Lie algebra of type A1 and nullity v with extended affine root system R(A1, S), where S is a semilattice in Rv, can be constructed from a TKK Lie algebra T(J(S)) which is obtained from the Jordan algebra J(S) by the so-called Tits-Kantor-Koecher construction. In this article we consider the Zn-graded automorphism group of the TKK Lie algebra T(J(S)), where S is the "smallest" semilattice in Euclidean space Rn.
Equations fonctionnelles et algèbres de Lie
Petracci, Emanuela
2003-01-01
In this thesis we study some algebraic problems which can be reduced to solving a functional equation. This technics allows us to get results which are new also for an ordinary Lie algebra and which are independent od the Lie algebra classification.; Dans cette thèse on a étudié plusieurs problèmesalgébriques relatifs à une superalgèbre de Lie qui peuvent êtreréduits à la résolution d'une équation fonctionnelle. Cettetechnique a permis d'obtenir des résultats qui sont nouveauxaussi pour une a...
q-deformed Lie algebras and fractional calculus
Herrmann, Richard
2007-01-01
Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. For the fractional harmonic oscillator, the corresponding q-number is derived. It is shown, that the resulting energy spectrum is an appropriate tool e.g. to describe the ground state spectra of even-even nuclei. In addition, the equivalence of rotational and vibrational spectra for fractional q-deformed Lie algebras is shown and the $B_\\alpha(E2)$ values for the fractional q-deformed symmetric rotor are calculated.
3D Object Recognition Based on Linear Lie Algebra Model
LI Fang-xing; WU Ping-dong; SUN Hua-fei; PENG Lin-yu
2009-01-01
A surface model called the fibre bundle model and a 3D object model based on linear Lie algebra model are proposed.Then an algorithm of 3D object recognition using the linear Lie algebra models is presented.It is a convenient recognition method for the objects which are symmetric about some axis.By using the presented algorithm,the representation matrices of the fibre or the base curve from only finite points of the linear Lie algebra model can be obtained.At last some recognition results of practicalities are given.
G-set Theory and Applications in Lie Theory
Aghayan, Reza
2012-01-01
This paper is devoted to the development and applications of some (new) basic concepts in Lie theory, both from `computational" and "observability" viewpoint. We specify set of all "G-equivariant" maps from a given Lie group G to the underlying manifold M, namely $G$-set, and also we introduce "conjugacy" in Lie group theory. The next goal of this paper is detailed analysis of the G-sets in connection with underlying transformation groups and providing a rigorous theoretical justification of "G-sets", when a group of transformations G acts on manifold M.
Wrapping Brownian motion and heat kernels I: compact Lie groups
Maher, David G
2010-01-01
An important object of study in harmonic analysis is the heat equation. On a Euclidean space, the fundamental solution of the associated semigroup is known as the heat kernel, which is also the law of Brownian motion. Similar statements also hold in the case of a Lie group. By using the wrapping map of Dooley and Wildberger, we show how to wrap a Brownian motion to a compact Lie group from its Lie algebra (viewed as a Euclidean space) and find the heat kernel. This is achieved by considering It\\^o type stochastic differential equations and applying the Feynman-Ka\\v{c} theorem.
On Split Lie Algebras with Symmetric Root Systems
Antonio J Calderón Martín
2008-08-01
We develop techniques of connections of roots for split Lie algebras with symmetric root systems. We show that any of such algebras is of the form $L=\\mathcal{U}+\\sum_j I_j$ with $\\mathcal{U}$ a subspace of the abelian Lie algebra and any $I_j$ a well described ideal of , satisfying $[I_j,I_k]=0$ if $j≠ k$. Under certain conditions, the simplicity of is characterized and it is shown that is the direct sum of the family of its minimal ideals, each one being a simple split Lie algebra with a symmetric root system and having all its nonzero roots connected.
Lie algebras determined by finite valued Auslander-Reiten quivers
张顺华
1997-01-01
Let r denote a connected valued Auslander-Reiten quiver,let (Γ) denote the free abelian group generated by the vertex set Γ0 and let Γ be the universal cover of Γ with fundamental group G.It is proved that when Γ is a finite connected valued Auslander-Reiten quiver,(Γ) is a Lie subalgebra of (Γ) and is just the "rbit" Lie algebra (Γ)/G,where (Γ)1 is the degenerate Hall algebra of Γ and (Γ)/G is the "orbit" Lie algebra induced by Γ.
Renormalization group flows and continual Lie algebras
Bakas, Ioannis
2003-01-01
We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time. We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches...
Classification of Hom-preLie Algebras in Dimension Two%二维Hom-preLie代数的分类
安慧辉; 康健; 王治淳
2014-01-01
In this paper, we mainly discuss the basic properties and the classification of Hom-Novikov algebras and Hom-preLie algebras in dimension two in the complex field. At first, we give the definition of the Hom-Novikov algebras, Hom-preLie algebras and some related defi-nitions. Then we discuss regular Hom-preLie algebras and give the necessary conditions for an Hom-preLie algebras to be pre-Lie type. We also give the direct sum of Hom-preLie alge-bras and get the necessary and sufficient condition for the existence of homomorphism between two Hom-preLie algebras. At last, with these definitions and their basic properties, we obtain the classification of the Hom-Novikov algebras and Hom-preLie algebras in two dimensions.%讨论了复数域上的二维Hom-Novikov 代数与Hom-preLie代数的基本性质以及分类。给出了Hom-Novikov 代数与Hom-preLie代数相关的一些基本定义和Hom-preLie是Pre-Lie型的必要条件；讨论Hom-preLie代数的直和，给出了两个Hom-preLie代数之间存在代数同态的充分必要条件。利用这些定义及其简单的性质，完成二维Hom-Novikov 代数与Hom-preLie代数的分类
Lie and Conditional Symmetries of a Class of Nonlinear (1 + 2-Dimensional Boundary Value Problems
Roman Cherniha
2015-08-01
Full Text Available A new definition of conditional invariance for boundary value problems involving a wide range of boundary conditions (including initial value problems as a special case is proposed. It is shown that other definitions worked out in order to find Lie symmetries of boundary value problems with standard boundary conditions, followed as particular cases from our definition. Simple examples of direct applicability to the nonlinear problems arising in applications are demonstrated. Moreover, the successful application of the definition for the Lie and conditional symmetry classification of a class of (1 + 2-dimensional nonlinear boundary value problems governed by the nonlinear diffusion equation in a semi-infinite domain is realised. In particular, it is proven that there is a special exponent, k ≠ —2, for the power diffusivity uk when the problem in question with non-vanishing flux on the boundary admits additional Lie symmetry operators compared to the case k ≠ —2. In order to demonstrate the applicability of the symmetries derived, they are used for reducing the nonlinear problems with power diffusivity uk and a constant non-zero flux on the boundary (such problems are common in applications and describing a wide range of phenomena to (1 + 1-dimensional problems. The structure and properties of the problems obtained are briefly analysed. Finally, some results demonstrating how Lie invariance of the boundary value problem in question depends on the geometry of the domain are presented.
Colour-kinematics duality and the Drinfeld double of the Lie algebra of diffeomorphisms
Fu, Chih-Hao; Krasnov, Kirill
2017-01-01
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.
Heiko Rauhut
Full Text Available Field experiments have shown that observing other people littering, stealing or lying can trigger own misconduct, leading to a decay of social order. However, a large extent of norm violations goes undetected. Hence, the direction of the dynamics crucially depends on actors' beliefs regarding undetected transgressions. Because undetected transgressions are hardly measureable in the field, a laboratory experiment was developed, where the complete prevalence of norm violations, subjective beliefs about them, and their behavioral dynamics is measurable. In the experiment, subjects could lie about their monetary payoffs, estimate the extent of liars in their group and make subsequent lies contingent on information about other people's lies. Results show that informed people who underestimate others' lying increase own lying more than twice and those who overestimate, decrease it by more than half compared to people without information about others' lies. This substantial interaction puts previous results into perspective, showing that information about others' transgressions can trigger dynamics in both directions: the spreading of normative decay and restoring of norm adherence.
Rauhut, Heiko
2013-01-01
Field experiments have shown that observing other people littering, stealing or lying can trigger own misconduct, leading to a decay of social order. However, a large extent of norm violations goes undetected. Hence, the direction of the dynamics crucially depends on actors' beliefs regarding undetected transgressions. Because undetected transgressions are hardly measureable in the field, a laboratory experiment was developed, where the complete prevalence of norm violations, subjective beliefs about them, and their behavioral dynamics is measurable. In the experiment, subjects could lie about their monetary payoffs, estimate the extent of liars in their group and make subsequent lies contingent on information about other people's lies. Results show that informed people who underestimate others' lying increase own lying more than twice and those who overestimate, decrease it by more than half compared to people without information about others' lies. This substantial interaction puts previous results into perspective, showing that information about others' transgressions can trigger dynamics in both directions: the spreading of normative decay and restoring of norm adherence.
Developments and retrospectives in Lie theory algebraic methods
Penkov, Ivan; Wolf, Joseph
2014-01-01
This volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics. Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Algebraic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current research. Mos...
Developments and retrospectives in Lie theory geometric and analytic methods
Penkov, Ivan; Wolf, Joseph
2014-01-01
This volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics. Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Geometric and Analytic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current re...
Geometric Approach to Lie Symmetry of Discrete Time Toda Equation
JIA Xiao-Yu; WANG Na
2009-01-01
By using the extended Harrison and Estabrook geometric approach,we investigate the Lie symmetry of discrete time Toda equation from the geometric point of view.Its one-dimensional continuous symmetry group is presented.
Intrinsic Optimal Control for Mechanical Systems on Lie Group
Chao Liu
2017-01-01
Full Text Available The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3, the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.
A Lie based 4-dimensional higher Chern-Simons theory
Zucchini, Roberto
2015-01-01
We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.
Entanglement between low- and high-lying atomic spin waves
Ding, D. S.; Wang, K.; Zhang, W.; Shi, S.; Dong, M. X.; Yu, Y. C.; Zhou, Z. Y.; Shi, B. S.; Guo, G. C.
2016-11-01
Establishing a quantum interface between different physical systems is of special importance for developing the practical versatile quantum networks. Entanglement between low- and high-lying atomic spin waves is essential for building up Rydberg-based quantum information engineering, which is also helpful to study the dynamics behavior of entanglement under external perturbations. Here, we report on the successful storage of a single photon as a high-lying atomic spin wave in a quantum regime. By storing a K-vector entanglement between a single photon and low-lying spin wave, we experimentally realize the entanglement between low- and high-lying atomic spin waves in two separated atomic systems. This makes our experiment a primary demonstration of Rydberg quantum memory of entanglement, representing a primary step toward the construction of a hybrid quantum interface.
Just-non-Lie nilpotent varieties of associative algebras
Finogenova, Olga
2011-01-01
We consider associative algebras over a field. An algebra variety is said to be {\\em Lie nilpotent} if it satisfies a polynomial identity of the kind $[x_1, x_2, ..., x_n] = 0$ where $[x_1,x_2] = x_1x_2 - x_2x_1$ and $[x_1, x_2, ..., x_n]$ is defined inductively by $[x_1, x_2, ..., x_n]=[[x_1, x_2, ..., x_{n-1}],x_n]$. It easy to see that every non-Lie nilpotent variety contains a minimal such subvariety. In the case of characteristic zero a complete description of the minimal non-Lie nilpotent (i.e. {\\em just-non-lie nilpotent}) varieties is found by Yu.Mal'cev. In the case of positive characteristic we reduce the problem of a description of such varieties to the case of {\\em prime} varieties.
Noncommutative Gravity and the *-Lie algebra of diffeomorphisms
Aschieri, P
2007-01-01
We construct functions and tensors on noncommutative spacetime by systematically twisting the corresponding commutative structures. The study of the deformed diffeomorphisms (and Poincare) Lie algebra allows to construct a noncomutative theory of gravity.
Noncommutative Gravity and the *-Lie algebra of diffeomorphisms
Aschieri, Paolo
2008-07-01
We construct functions and tensors on noncommutative spacetime by systematically twisting the corresponding commutative structures. The study of the deformed diffeomorphisms (and Poincaré) Lie algebra allows to construct a noncomutative theory of gravity.
Transitive Lie groups on S^1\\times S^{2m}
Gorbatsevich, Vladimir V.
2007-10-01
The structure of Lie groups acting transitively on the direct product of a circle and an even-dimensional sphere is described. For products of two spheres of dimension >1 a similar problem has already been solved by other authors. The minimal transitive Lie groups on S^1 and S^{2m} are also indicated. As an application of these results, the structure of the automorphism group of one class of geometric structures, generalized quadrangles (a special case of Tits buildings) is considered. A conjecture put forward by Kramer is proved: the automorphism group of a connected generalized quadrangle of type (1,2m) always contains a transitive subgroup that is the direct product of a compact simple Lie group and a one-dimensional Lie group. Bibliography: 16 titles.
Leibniz algebras associated with representations of filiform Lie algebras
Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.
2015-12-01
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.
Calculations on Lie Algebra of the Group of Affine Symplectomorphisms
Zuhier Altawallbeh
2017-01-01
Full Text Available We find the image of the affine symplectic Lie algebra gn from the Leibniz homology HL⁎(gn to the Lie algebra homology H⁎Lie(gn. The result shows that the image is the exterior algebra ∧⁎(wn generated by the forms wn=∑i=1n(∂/∂xi∧∂/∂yi. Given the relevance of Hochschild homology to string topology and to get more interesting applications, we show that such a map is of potential interest in string topology and homological algebra by taking into account that the Hochschild homology HH⁎-1(U(gn is isomorphic to H⁎-1Lie(gn,U(gnad. Explicitly, we use the alternation of multilinear map, in our elements, to do certain calculations.
Gruppi, anelli di Lie e teoria della coomologia
Zappa, G
2011-01-01
This book includes: R. Baer: Complementation in finite gropus; M. Lazard: Groupes, anneaux de Lie et probleme de Burnside; J. Tits: Sur les groupes algebriques afffines; Theoremes fondamentaux de structure; and, Classification des groupes semisimples et geometries associees.
Lie symmetries of the geodesic equations and projective collineations
Tsamparlis, Michael; Paliathanasis, Andronikos, E-mail: mtsampa@phys.uoa.g, E-mail: paliathanasis@gmail.co [Department of Physics, Section Astrophysics Astronomy Mechanics, University of Athens, University of Athens, Zografos 15783, Athens (Greece)
2009-10-01
We study the Lie symmetries of the geodesic equations in a Riemannian space and show that they coincide with the projective symmetries of the Riemannian metric. We apply the result to the spaces of constant curvature.
On Complete Lie Algebras and Lie Groups%关于完备李群与完备李代数
梁科; 邓少强
2001-01-01
孟道骥等对完备李代数作了系统的研究并已获得很多基本和重要的结果.本文给出完备李群与完备李代数的某些关系.%Daoji Meng and others have made a systematic study on complete Lie algebras and obtained some basic and important conclusions. In this paper, we will investigate relations between complete Lie groups and complete Lie algebras.
How to Accuse the Other Guy of Lying with Statistics
Murray, Charles
2005-01-01
We’ve known how to lie with statistics for 50 years now. What we really need are theory and praxis for accusing someone else of lying with statistics. The author’s experience with the response to The Bell Curve has led him to suspect that such a formulation already exists, probably imparted during a secret initiation for professors in the social sciences. This article represents his best attempt to reconstruct what must be in it.
Compact Lie groups: Euler constructions and generalized Dyson conjecture
Cacciatori, S L; Scotti, A
2012-01-01
In this paper we present a very general method to construct generalized Euler parameterizations for compact simple Lie groups w.r.t. maximally symmetrically embedded simple Lie groups. Our construction is based on a detailed analysis of the geometry of these groups, which moreover gives rise to an interesting connection with certain generalized Dyson integrals. In particular, we obtain a geometry based proof of the generalized Macdonald conjecture correspondent to the root systems associated to all irreducible symmetric spaces.
Simple Lie algebras arising from Leavitt path algebras
Abrams, Gene
2011-01-01
For a field K and directed graph E, we analyze those elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E), L_K(E)]. This analysis allows us to give easily computable necessary and sufficient conditions to determine which Lie algebras of the form [L_K(E), L_K(E)] are simple, when E is row-finite and L_K(E) is simple.
On the low-lying states of TiC
Bauschlicher, C. W., Jr.; Siegbahn, P. E. M.
1984-01-01
The ground and low-lying excited states of TiC are investigated using a CASSCF-externally contracted CI approach. The calculations yield a 3Sigma(+) ground state, but the 1Sigma(+) state is only 780/cm higher and cannot be ruled out. The low-lying states have some triple bond character. The nature of the bonding and origin of the states are discussed.
On the low-lying states of TiC
Bauschlicher, C. W., Jr.; Siegbahn, P. E. M.
1984-01-01
The ground and low-lying excited states of TiC are investigated using a CASSCF-externally contracted CI approach. The calculations yield a 3Sigma(+) ground state, but the 1Sigma(+) state is only 780/cm higher and cannot be ruled out. The low-lying states have some triple bond character. The nature of the bonding and origin of the states are discussed.
Lie detection: an overview of difficulties, pitfalls, and people's ability
Vrij, Aldert
2004-01-01
People generally find it difficult to distinguish between truth and falsehood, as we demonstrate in first part of this article. This is validated every day, not only to laymen but also that of professionals in detecting lies (police detectives, customs officers and so on). In the second part of the article we will do an overview of the many causes and reasons for people are deficient in detecting truths and lies.
Monomial bases for free pre-Lie algebras
al-Kaabi, Mahdi Jasim Hasan
2013-01-01
In this paper, we study the concept of free pre-Lie algebra generated by a (non-empty) set. We review the construction of A. Agrachev and R. Gamkrelidze of monomial bases in free pre-Lie algebras. We describe the matrix of the monomial basis vectors in terms of the rooted trees basis exhibited by F. Chapoton and M. Livernet. We also show that this matrix is unipotent and we find an explicit expression for its coefficients.
限制李三系的半单元%Semisimple Elements of Restricted Lie Triple Systems
刘秀娟; 陈良云
2012-01-01
The present paper is devoted to some elementary properties of semisimple elements for restricted Lie triple systems. We give some conditions for the commutativity of restricted Lie triple systems, obtain some conditions for which a restricted Lie triple systems possesses a basis consisting of toral elements and characterize some properties of Frattini p-subsystem for restricted Lie triple systems. Moreover, we study some elementary properties of semisimple elements for semisimple restricted Lie triple systems.%研究了限制李三系的半单元的一些重要性质,给出了若干个限制李三系是可换的条件,得到了限制李三系的有环面元基的几个条件,刻划了限制李三系的Frattini p-子系的一些性质.同时,研究了中心为零的所有元素是半单元的限制李三系的一些重要性质.
Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras
Ammar, F [Faculte des Sciences, Universite de Sfax, BP 1171, 3000 Sfax (Tunisia); Makhlouf, A [Laboratoire de Mathematiques, Informatique et Applications, Universite de Haute Alsace, 4, rue des Freres Lumiere F-68093 Mulhouse (France); Silvestrov, S, E-mail: Faouzi.Ammar@rnn.fss.t, E-mail: Abdenacer.Makhlouf@uha.f, E-mail: sergei.silvestrov@math.lth.s [Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund (Sweden)
2010-07-02
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.
Emotion and lying in a non-native language.
Caldwell-Harris, Catherine L; Ayçiçeği-Dinn, Ayşe
2009-03-01
Bilingual speakers frequently report experiencing greater emotional resonance in their first language compared to their second. In Experiment 1, Turkish university students who had learned English as a foreign language had reduced skin conductance responses (SCRs) when listening to emotional phrases in English compared to Turkish, an effect which was most pronounced for childhood reprimands. A second type of emotional language, reading out loud true and false statements, was studied in Experiment 2. Larger SCRs were elicited by lies compared to true statements, and larger SCRs were evoked by English statements compared to Turkish statements. In contrast, ratings of how strongly participants felt they were lying showed that Turkish lies were more strongly felt than English lies. Results suggest that two factors influence the electrodermal activity elicited when bilingual speakers lie in their two languages: arousal due to emotions associated with lying, and arousal due to anxiety about managing speech production in non-native language. Anxiety and emotionality when speaking a non-naive language need to be better understood to inform practices ranging from bilingual psychotherapy to police interrogation of suspects and witnesses.
In vino veritas? Alcohol, response inhibition and lying.
Suchotzki, Kristina; Crombez, Geert; Debey, Evelyne; van Oorsouw, Kim; Verschuere, Bruno
2015-01-01
Despite the widespread belief that alcohol makes the truth come out more easily, we know very little on how alcohol impacts deception. Given that alcohol impairs response inhibition, and that response inhibition may be critically involved in deception, we expected that alcohol intake would hamper lying. In total, 104 volunteers were tested at a science festival, where they had the opportunity to drink alcohol. Stop-Signal Reaction Times (SSRTs) served as operationalization of response inhibition. Differences in error rates and reaction times (RTs) between lying and truth telling served as indicators of the cognitive cost of lying. Higher blood alcohol concentration was related to longer SSRTs, but unrelated to the cognitive costs of lying. This study validates previous laboratory research on alcohol and response inhibition in a realistic drinking environment, yet failed to find an effect of alcohol on lying. Implications of these findings and for the role of response inhibition in lying are discussed. © The Author 2014. Medical Council on Alcohol and Oxford University Press. All rights reserved.
A new approach to tolerance analysis method based onthe screw and the Lie Algebra of Lie Group
Zhai, X. C.; Du, Q. G.; Wang, W. X.; Wen, Q.; Liu, B. S.; Sun, Z. Q.
2016-11-01
Tolerance analysis refers to the process of establishing mapping relations between tolerance features and the target feature along the dimension chain. Traditional models for tolerance analysis are all based on rigid body kinematics, and they adopt the Homogeneous Transformation Matrix to describe feature variation and accumulation. However, those models can hardly reveal the nature of feature variations. This paper proposes a new tolerance analysis method based on the screw and the Lie Algebra of Lie Group, which describes feature variation as the screw motion, and completely maps the twist, an element of the Lie Algebra, to the Lie Group that represents the feature configuration space. Thus, the analysis can be conducted in a more succinct and direct way. In the end, the method is applied in an example and proven to be robust and effective.
A pilot study on the improvement of the lying area of finishing pigs by a soft lying mat.
Savary, Pascal; Gygax, Lorenz; Jungbluth, Thomas; Wechsler, Beat; Hauser, Rudolf
2011-01-01
In this pilot study, we tested whether a soft mat (foam covered with a heat-sealed thermoplastic) reduces alterations and injuries at the skin and the leg joints.The soft mat in the lying area of partly slatted pens was compared to a lying area consisting of either bare or slightly littered (100 g straw per pig and day) concrete flooring. In this study we focused on skin lesions on the legs of finishing pigs as indicators of impaired welfare. Pigs were kept in 19 groups of 8-10 individuals and were examined for skin lesions around the carpal and tarsal joints either at a weight of concrete floor. Pens with a littered concrete floor did not differ compared to pens with a bare concrete floor. The soft lying mat thus improved floor quality in the lying area in terms of preventing skin lesions compared to bare and slightly littered concrete flooring. Such soft lying mats have thus the potential to improve lying comfort and welfare of finishing pigs.
L1-determined ideals in group algebras of exponential Lie groups
Ungermann, Oliver
2012-01-01
A locally compact group $G$ is said to be $\\ast$-regular if the natural map $\\Psi:\\Prim C^\\ast(G)\\to\\Prim_{\\ast} L^1(G)$ is a homeomorphism with respect to the Jacobson topologies on the primitive ideal spaces $\\Prim C^\\ast(G)$ and $\\Prim_{\\ast} L^1(G)$. In 1980 J. Boidol characterized the $\\ast$-regular ones among all exponential Lie groups by a purely algebraic condition. In this article we introduce the notion of $L^1$-determined ideals in order to discuss the weaker property of primitive $\\ast$-regularity. We give two sufficient criteria for closed ideals $I$ of $C^\\ast(G)$ to be $L^1$-determined. Herefrom we deduce a strategy to prove that a given exponential Lie group is primitive $\\ast$-regular. The author proved in his thesis that all exponential Lie groups of dimension $\\le 7$ have this property. So far no counter-example is known. Here we discuss the example $G=B_5$, the only critical one in dimension $\\le 5$.
Deceit and dishonesty as practice: the comfort of lying.
Carter, Melody
2016-07-01
Lying and deceit are instruments of power, used by social actors in the pursuit of their practices as they seek to maintain social order. All social actors, nurses included, have deceit and dishonesty within their repertoire of practice. Much of this is benign, well intentioned and a function of being sociable and necessary in the pursuit of social order in the healthcare environment. Lying and deceit from a sociological point of view, is a reflection of the different modes of domination that exist within a social space. French philosopher Pierre Bourdieu theorized about the way that symbolic power works within social space. The social structures and the agency of individual actors moving within it are interrelated and interdependent. Bourdieu's ideas will be used to theorize about real clinical experiences where acts of deceit can be identified and a case example will be presented. Nurses are actors in the social space of clinical care, and their world is complex, challenging, and often fraught with the contradictory demands and choices that reflect and influence their behaviours. An exploration of lying and deceit in nursing as an instrument in the modes of domination that persist enables us to challenge some of the assumptions that are made about the motives that cause or tempt nurses to lie as well as to understand the way on which they are sometimes lied to, according to the acts of domination that exist in the field. Lying or acting dishonestly is a powerful act that is intent on retaining stability and social order and could be seen to be a justification of lying and deceit. However, we need to pause and consider, in whose interests are we striving to create social order? Is it in the end about the comfort of patients or for the comfort of professionals?
Zhu, Huangjun
2014-09-01
Generalized symmetric informationally complete (SIC) measurements are SIC measurements that are not necessarily rank 1. They are interesting originally because of their connection with rank-1 SICs. Here we reveal several merits of generalized SICs in connection with quantum state tomography and Lie algebra that are interesting in their own right. These properties uniquely characterize generalized SICs among minimal informationally complete (IC) measurements although, on the face of it, they bear little resemblance to the original definition. In particular, we show that in quantum state tomography generalized SICs are optimal among minimal IC measurements with given average purity of measurement outcomes. Besides its significance to the current study, this result may help us to understand tomographic efficiencies of minimal IC measurements under the influence of noise. When minimal IC measurements are taken as bases for the Lie algebra of the unitary group, generalized SICs are uniquely characterized by the antisymmetry of the associated structure constants.
A representation of Weyl-Heisenberg Lie algebra in the quaternionic setting
Muraleetharan, B.; Thirulogasanthar, K.; Sabadini, I.
2017-10-01
Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the so-obtained position and momentum operators, we study the Heisenberg uncertainty principle on the whole set of quaternions and on a quaternionic slice, namely on a copy of the complex plane inside the quaternions. For the quaternionic harmonic oscillator, the uncertainty relation is shown to saturate on a neighborhood of the origin in the case we consider the whole set of quaternions, while it is saturated on the whole slice in the case we take the slice-wise approach. In analogy with the complex Weyl-Heisenberg Lie algebra, Lie algebraic structures are developed for the quaternionic case. Finally, we introduce a quaternionic displacement operator which is square integrable, irreducible and unitary, and we study its properties.
Partition functions for quantum gravity, black holes, elliptic genera and Lie algebra homologies
Bonora, L., E-mail: bonora@sissa.it [International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste (Italy); INFN, Sezione di Trieste (Italy); Bytsenko, A.A., E-mail: abyts@uel.br [Departamento de Fisica, Universidade Estadual de Londrina, Caixa Postal 6001, Londrina (Brazil)
2011-11-11
There is a remarkable connection between quantum generating functions of field theory and formal power series associated with dimensions of chains and homologies of suitable Lie algebras. We discuss the homological aspects of this connection with its applications to partition functions of the minimal three-dimensional gravities in the space-time asymptotic to AdS{sub 3}, which also describe the three-dimensional Euclidean black holes, the pure N=1 supergravity, and a sigma model on N-fold generalized symmetric products. We also consider in the same context elliptic genera of some supersymmetric sigma models. These examples can be considered as a straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to partition functions represented by means of formal power series that encode Lie algebra properties.
Lie Symmetries and Conserved Quantities for Super-Long Elastic Slender Rod
ZHAO Wei-Jia; WENG Yu-Quan; FU Jing-Li
2007-01-01
DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. We study the Lie symmetries of a super-long elastic slender rod by using the methods of infinitesimal transformation. Based on Kirchhoff's analogue, generalized Hamilton canonical equations are analysed. The infinitesimal transformations with respect to the radian coordinate, the generalized coordinate, and the quasimomentum of the model are introduced. The Lie symmetries and conserved quantities of the model are presented.
Simplicities and Automorphisms of a Sp ecial Infinite Dimensional Lie Algebra
YU De-min; LI Ai-hua
2013-01-01
In this paper, a special infinite dimensional Lie algebra is studied. The infinite dimensional Lie algebra appears in the fields of conformal theory, mathematical physics, statistic mechanics and Hamilton operator. The infinite dimensional Lie algebras is pop-ularized Virasoro-like Lie algebra. Isomorphisms, homomorphisms, ideals of the infinite dimensional Lie algebra are studied.
Controllability of affine right-invariant systems on solvable Lie groups
Yuri L. Sachkov
1997-12-01
Full Text Available The aim of this paper is to present some recent results on controllability of right-invariant systems on Lie groups. From the Lie-theoretical point of view, we study conditions under which subsemigroups generated by half-planes in the Lie algebra of a Lie group coincide with the whole Lie group.
Ombud’s Corner: a world without lies?
Sudeshna Datta-Cockerill
2016-01-01
Can a world without lies exist? Are there different types of lies, some more acceptable than others, or is that just an excuse that we use to justify ourselves? What consequences do lies have in the working environment? If we look in the dictionary for the definition of “lie”, we find: “A lie is a false statement made with deliberate intent to deceive”. This simple definition turns out to be very useful when we feel stuck in intricate conflict situations where we suspect lies to have played a role. Examples may include supervisors presenting a situation in different ways to different colleagues; colleagues withholding information that could be useful to others; reports given in a non-accurate way; and rumours that spread around but cannot be verified. Peter was very keen to lead a particular project. He spoke to his supervisor Philippe who told him that he had in fact already proposed him to the board. When he did not get the job, Peter shared h...
On squares of representations of compact Lie algebras
Zeier, Robert, E-mail: robert.zeier@ch.tum.de [Department Chemie, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching (Germany); Zimborás, Zoltán, E-mail: zimboras@gmail.com [Department of Computer Science, University College London, Gower St., London WC1E 6BT (United Kingdom)
2015-08-15
We study how tensor products of representations decompose when restricted from a compact Lie algebra to one of its subalgebras. In particular, we are interested in tensor squares which are tensor products of a representation with itself. We show in a classification-free manner that the sum of multiplicities and the sum of squares of multiplicities in the corresponding decomposition of a tensor square into irreducible representations has to strictly grow when restricted from a compact semisimple Lie algebra to a proper subalgebra. For this purpose, relevant details on tensor products of representations are compiled from the literature. Since the sum of squares of multiplicities is equal to the dimension of the commutant of the tensor-square representation, it can be determined by linear-algebra computations in a scenario where an a priori unknown Lie algebra is given by a set of generators which might not be a linear basis. Hence, our results offer a test to decide if a subalgebra of a compact semisimple Lie algebra is a proper one without calculating the relevant Lie closures, which can be naturally applied in the field of controlled quantum systems.
Discussions About Lying With An Ethical Reasoning Robot
Bentzen, Martin Mose; Lindner, Felix; Wächter, Laura
The conversational ethical reasoning robot Immanuel is presented. Immanuel is capable of defending multiple ethical views on morally delicate situations. A study was conducted to evaluate the acceptance of Immanuel. The participants had a conversation with the robot on whether lying is permissibile...... in a given situation. The robot first signaled uncertainty about whether lying is right or wrong in the situation, then disagreed with the participant’s view, and finally asked for justification. The results indicate that participants with a higher tendency to utilitarian judgments are initially more certain...... about their view as compared to participants with a higher tendency to deontological judgments. These differences vanish at the end of the dialogue. Lying is defended and argued against by both utilitarian and deontologically oriented participants. The diversity of the reported arguments gives an idea...
Virial theorem in quasi-coordinates and Lie algebroid formalism
Cariñena, José F.; Gheorghiu, Irina; Martínez, Eduardo; Santos, Patrícia
2014-04-01
In this paper, the geometric approach to the virial theorem (VT) developed in [J. F. Cariñena, F. Falceto and M. F. Rañada, A geometric approach to a generalized virial theorem, J. Phys. A: Math. Theor. 45 (2012) 395210, 19 pp.] is written in terms of quasi-velocities (see [J. F. Cariñena, J. Nunes da Costa and P. Santos, Quasi-coordinates from the point of view of Lie algebroid structures, J. Phys. A: Math. Theor. 40 (2007) 10031-10048]). A generalization of the VT for mechanical systems on Lie algebroids is also given, using the geometric tools of Lagrangian and Hamiltonian mechanics on the prolongation of the Lie algebroid.
What Goes Around, Comes Around: Experimental Evidence on Exposed Lies
Sarah Mörtenhuber
2016-10-01
Full Text Available We experimentally investigate the optimal way to handle the uncovering of a noble lie, that is, a lie that supposedly is in the best interest of a given community. For this purpose, we analyze a public good game with feedback to group members on the average contributions of the other group members. The computer program inflates the feedback and shows higher than real average contributions to the high contributors. As shown by earlier studies, the partial feedback inflation increases the total payoff of the public good as it avoids the feeling of being a sucker for above average contributors. The lie is then uncovered and we continue with different feedback modes on contributions, some inflated, some true. We find that players respond similarly to both feedback modes. However, with true feedback, initial contributions in the second stage are significantly higher than with inflated feedback.
11th Workshop Lie Theory and Its Applications in Physics
LT-11
2016-01-01
This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.< This is a large interdisciplinary a...
Prospects of functional Magnetic Resonance Imaging as lie detector
Elena eRusconi
2013-09-01
Full Text Available Following the demise of the polygraph, supporters of assisted scientific lie detection tools have enthusiastically appropriated neuroimaging technologies as the savior of scientifically verifiable lie detection in the courtroom (Gerard, 2008: 5; however, such enthusiasm may prove premature. For in nearly every article published by independent researchers in peer reviewed journals, the respective authors acknowledge that fMRI research, processes, and technology are insufficiently developed and understood for gatekeepers to even consider introducing these neuroimaging measures into criminal courts as they stand today for the purpose of determining the veracity of statements made. Regardless of how favorable their analyses of fMRI or its future potential, they all acknowledge the presence of issues yet to be resolved. Even assuming a future where these issues are resolved and an appropriate fMRI lie-detection process is developed, its integration into criminal trials is not assured for the very success of such a future system may necessitate its exclusion from courtrooms on the basis of existing legal and ethical prohibitions. In this piece, aimed for a multidisciplinary readership, we seek to highlight and bring together the multitude of hurdles which would need to be successfully overcome before fMRI can (if ever be a viable applied lie detection system. We argue that the current status of fMRI studies on lie detection meets neither basic legal nor scientific standards. We identify four general classes of hurdles (scientific, legal and ethical, operational, and social and provide an overview on the stages and operations involved in fMRI studies, as well as the difficulties of translating these laboratory protocols into a practical criminal justice environment. It is our overall conclusion that fMRI is unlikely to constitute a viable lie detector for criminal courts.
Applications of Lie Symmetries to Higher Dimensional Gravitating Fluid
Msomi, A M; Maharaj, S D
2013-01-01
We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie point symmetries of the fundamental field equation, we obtain either an implicit solution or we can reduce the governing equations to a Riccati equation. We show that known solutions of the Einstein equations can produce infinite families of new solutions. Earlier results in four dimensions are shown to be special cases of our generalised results.
Lie Groupoids in Classical Field Theory I: Noether's Theorem
Costa, Bruno T; Pêgas, Luiz Henrique P
2015-01-01
In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. Here, we outline the basis of the program and, as a first step, show how to (re)formulate Noether's theorem about the connection between symmetries and conservation laws in this approach.
Application of Lie group analysis in geophysical fluid dynamics
Ibragimov, Ranis
2011-01-01
This is the first monograph dealing with the applications of the Lie group analysis to the modeling equations governing internal wave propagation in the deep ocean. A new approach to describe the nonlinear interactions of internal waves in the ocean is presented. While the central idea of the book is to investigate oceanic internal waves through the prism of Lie group analysis, it is also shown for the first time that internal wave beams, representing exact solutions to the equation of motion of stratified fluid, can be found by solving the given model as invariant solutions of nonlinear equat
Characteristic Classes and Integrable Systems for Simple Lie Groups
Levin, A; Smirnov, A; Zotov, A
2010-01-01
This paper is a continuation of our previous paper \\cite{LOSZ}. For simple complex Lie groups with non-trivial center, i.e. classical simply-connected groups, $E_6$ and $E_7$ we consider elliptic Modified Calogero-Moser systems corresponding to the Higgs bundles with an arbitrary characteristic class. These systems are generalization of the classical Calogero-Moser (CM) systems related to a simple Lie groups and contain CM systems related to some (unbroken) subalgebras. For all algebras we construct a special basis, corresponding to non-trivial characteristic classes, the explicit forms of Lax operators and Hamiltonians.
Applications of Lie Group Integrators and Exponential Schemes
2007-11-02
Classical numerical ODE-solvers progress solution along straight lines. • Lie group integrators map a straight line in some other space (Lie algebra) to...term. Includes: NLS, Nonlinear heat equations , KdV , Allen–Cahn, Kuramoto–Sivashinsky, and many more. Unbounded L requires a form of implicit integrator...variational equation Mdzt + Kdzx = DzzS(z)dz It easily follows that this pair of solutions satisfies ∂tω(U, V ) + ∂xκ(U, V ) = 0 the symplectic conservation law
Second cohomology of Lie rings and the Schur multiplier
Max Horn
2014-06-01
Full Text Available We exhibit an explicit construction for the second cohomology group$H^2(L, A$ for a Lie ring $L$ and a trivial $L$-module $A$.We show how the elements of $H^2(L, A$ correspond one-to-one to theequivalence classes of central extensions of $L$ by $A$, where $A$now is considered as an abelian Lie ring. For a finite Liering $L$ we also show that $H^2(L, C^* cong M(L$, where $M(L$ denotes theSchur multiplier of $L$. These results match precisely the analoguesituation in group theory.
Solvable Lie algebras with naturally graded nilradicals and their invariants
Ancochea, J M; Campoamor-Stursberg, R; Vergnolle, L Garcia [Departamento GeometrIa y TopologIa, Fac. CC. Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias 3, E-28040 Madrid (Spain)
2006-02-10
The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analysed, and their generalized Casimir invariants are calculated. It is shown that rank one solvable algebras have a contact form, which implies the existence of an associated dynamical system. Moreover, due to the structure of the quadratic Casimir operator of the nilradical, these algebras contain a maximal non-abelian quasi-classical Lie algebra of dimension 2n - 1, indicating that gauge theories (with ghosts) are possible on these subalgebras.
Internal labelling operators and contractions of Lie algebras
Campoamor-Stursberg, R [Dpto. GeometrIa y TopologIa, Fac. CC. Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias, 3, E-28040 Madrid (Spain)
2007-12-07
We analyse under which conditions the missing label problem associated with a reduction chain s' subset of s of (simple) Lie algebras can be completely solved by means of an Inoenue-Wigner contraction g naturally related to the embedding. This provides a new interpretation of the missing label operators in terms of the Casimir operators of the contracted algebra, and shows that the available labelling operators are not completely equivalent. Further, the procedure is used to obtain upper bounds for the number of invariants of affine Lie algebras arising as contractions of semi-simple algebras.
Lie symmetry analysis and explicit solutions of the time fractional fifth-order KdV equation.
Gang Wei Wang
Full Text Available In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last, by virtue of the sub-equation method, some exact solutions to the fractional fifth-order KdV equation are provided.
Lie symmetry analysis and explicit solutions of the time fractional fifth-order KdV equation.
Wang, Gang Wei; Xu, Tian Zhou; Feng, Tao
2014-01-01
In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last, by virtue of the sub-equation method, some exact solutions to the fractional fifth-order KdV equation are provided.
Dobrev, V K
2013-01-01
In the present paper we review the progress of the project of classification and construction of invariant differential operators for non-compact semisimple Lie groups. Our starting points is the class of algebras, which we called earlier 'conformal Lie algebras' (CLA), which have very similar properties to the conformal algebras of Minkowski space-time, though our aim is to go beyond this class in a natural way. For this we introduced recently the new notion of {\\it parabolic relation} between two non-compact semisimple Lie algebras $\\cal G$ and $\\cal G'$ that have the same complexification and possess maximal parabolic subalgebras with the same complexification. Thus, we consider the exceptional algebra $E_{7(7)}$ which is parabolically related to the CLA $E_{7(-25)}$. Other interesting examples are the orthogonal algebras $so(p,q)$ all of which are parabolically related to the conformal algebra $so(n,2)$ with $p+q=n+2$, the parabolic subalgebras including the Lorentz subalgebra $so(n-1,1)$ and its analogs ...
Exceptional Lie Groups, E-infinity Theory and Higgs Boson
El-Okaby, Ayman A
2007-01-01
In this paper, we study the correlation between the exceptional lie groups and El-Naschie's transfinite E-infinity spacetime theory. Subsequently this is used to calculate the number of elementary particles in the standard model, mass of the Higgs boson and some coupling constants.
Exceptional Lie groups, E-infinity theory and Higgs Boson
El-Okaby, Ayman A. [Department of Physics, Faculty of Science, Alexandria University (Egypt)], E-mail: elokaby@yahoo.com
2008-12-15
In this paper we study the correlation between El-Naschie's exceptional Lie groups hierarchies and his transfinite E-infinity space-time theory. Subsequently this correlation is used to calculate the number of elementary particles in the standard model, mass of the Higgs Bosons and some coupling constants.
Characterization of Lie Higher Derivations on Triangular Algebras
Xiao Fei QI
2013-01-01
Let A and B be unital rings,and M be an (A,B)-bimodule,which is faithful as a left A-module and also as a right B-module.Let U =Tri(A,M,B) be the triangular algebra.In this paper,we give some different characterizations of Lie higher derivations on U.
Fixed Points of -Endomorphisms of a Free Metabelian Lie Algebra
Naime Ekici; Demet Parlak Sönmez
2011-11-01
Let be a free metabelian Lie algebra of finite rank at least 2. We show the existence of non-trivial fixed points of an -endomorphism of and give an algorithm detecting them. In particular, we prove that the fixed point subalgebra Fix of an -endomorphism of is not finitely generated.
Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras
Luigi Accardi
2009-05-01
Full Text Available The present paper reviews some intriguing connections which link together a new renormalization technique, the theory of *-representations of infinite dimensional *-Lie algebras, quantum probability, white noise and stochastic calculus and the theory of classical and quantum infinitely divisible processes.
An Identity with Skew Derivations on Lie Ideals
Wang Zheng-ping; Rehman Ur Nadeem; Huang Shu-liang
2016-01-01
Let R be a 2-torsion free prime ring and L a noncommutative Lie ideal of R. Suppose that (d,σ) is a skew derivation of R such that xsd(x)xt = 0 for all x∈L, where s, t are fixed non-negative integers. Then d=0.
Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics
Alex J. Dragt; Filippo Neri; Govindan Rangarajan; David Douglas; Liam M. Healy; Robert D. Ryne
1988-12-01
The purpose of this paper is to present a summary of new methods, employing Lie algebraic tools, for characterizing beam dynamics in charged-particle optical systems. These methods are applicable to accelerator design, charged-particle beam transport, electron microscopes, and also light optics. The new methods represent the action of each separate element of a compound optical system, including all departures from paraxial optics, by a certain operator. The operators for the various elements can then be concatenated, following well-defined rules, to obtain a resultant operator that characterizes the entire system. This paper deals mostly with accelerator design and charged-particle beam transport. The application of Lie algebraic methods to light optics and electron microscopes is described elsewhere (1, see also 44). To keep its scope within reasonable bounds, they restrict their treatment of accelerator design and charged-particle beam transport primarily to the use of Lie algebraic methods for the description of particle orbits in terms of transfer maps. There are other Lie algebraic or related approaches to accelerator problems that the reader may find of interest (2). For a general discussion of linear and nonlinear problems in accelerator physics see (3).
Lie algebras and degenerate Affine Hecke Algebras of type A
Arakawa, T
1997-01-01
We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simple H-module can be thus obtained.
Quantum Poisson-Lie T-duality and WZNW model
Alekseev, A Yu; Tseytlin, Arkady A
1996-01-01
A pair of conformal sigma models related by Poisson-Lie T-duality is constructed by starting with the O(2,2) Drinfeld double. The duality relates the standard SL(2,R) WZNW model to a constrained sigma model defined on SL(2,R) group space. The quantum equivalence of the models is established by using a path integral argument.
Derivations as Homomorphisms or Anti-homomorphisms on Lie Ideals
Yu WANG; Hong YOU
2007-01-01
Let R be a 2-torsion free prime ring, Z the center of R,and U a nonzero Lie ideal of R.If d is a derivation of R which acts as a homomorphism or an anti-homomorphism on U, then either d=0 or U(∈)Z.This result improves a theorem of Asma, Rehman,and Shakir.
Locally operating realizations of nonconnected transformation Lie groups
García-Prada, Oscar; del Olmo, Mariano A.; Santander, Mariano
1988-05-01
A systematic study of locally operating multiplier realizations of nonconnected Lie groups of transformations is presented that generalizes previous results on connected groups. The semilinear locally operating multiplier realizations of a nonconnected group G are those obtained through an induction process from the finite-dimensional semilinear representations of a given subgroup of a representation group Ḡ for G.
Continual Lie algebras and noncommutative counterparts of exactly solvable models
Zuevsky, A.
2004-01-01
Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.
Essays in the history of Lie groups and algebraic groups
Borel, Armand
2001-01-01
Lie groups and algebraic groups are important in many major areas of mathematics and mathematical physics. We find them in diverse roles, notably as groups of automorphisms of geometric structures, as symmetries of differential systems, or as basic tools in the theory of automorphic forms. The author looks at their development, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. Starting from Lie's theory of local analytic transformation groups and early work on Lie algebras, he follows the process of globalization in its two main frameworks: differential geometry and topology on one hand, algebraic geometry on the other. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter. The essays in the first part of the book survey various proofs of the full reducibility of linear representations of \\mathbf{SL}_2{(\\mathbb{C})}, the contributions of H. Weyl to representations and invariant theory for semisimple Lie groups, and con...
The Low-Lying Electronic States of Mg2(+)
Ricca, Alessandra; Bauschlicher, Charles W., Jr.
1994-01-01
The low-lying doublet and quartet states of Mg+ have been studied using a multireference configuration interaction approach. The effect of inner-shell correlation has been included using the core-polarization potential method. The computed spectroscopic constants, lifetimes, and oscillator strengths should help resolve the difference between the recent experiments and previous theoretical calculations.
Lying Behavior, Family Functioning and Adjustment in Early Adolescence
Engels, Rutger C. M. E.; Finkenauer, Catrin; van Kooten, Dyana C.
2006-01-01
Communication between children and parents has been the subject of several studies, examining the effects of, for example, disclosure and secrecy on adolescents' social relationships and adjustment. Less attention has paid to adolescent deception. We developed and tested a new instrument on lying behavior in a sample of 671 parent-adolescent…
Almost Lie structures on an anchored Banach bundle
Cabau, Patrick
2011-01-01
Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bundles and the relation between these objects. We then obtain an adapted formalism for mechanical systems which is illustrated by the evolutionary problem of the "Hilbert snake"
An Algorithm for the Decomposition of Semisimple Lie Algebras
Graaf, W.A. de
2001-01-01
We consider the problem of decomposing a semisimple Lie algebra dened over a eld of characteristic zero as a direct sum of its simple ideals The method is based on the decomposition of the action of a Cartan subalgebra An implementation of the algorithm in the system ELIAS is discussed at the end of
Exceptional groups of Lie type and flag-transitive triplanes
无
2010-01-01
A triplane is a ( v, k, 3)-symmetric design. Let G be a subgroup of the full automorphism group of a triplane D. In this paper we prove that if G is flag-transitive and point-primitive, then the socle of G cannot be a simple exceptional group of Lie type.
Leibniz Central Extension on a Block Lie Algebra
Qing Wang; Shaobin Tan
2007-01-01
Let B be the Lie algebra over C with basis {Lm,n | m, n ∈ Z, n≥0} and relations [Lm,n,Lm1 ,n1 ]=((n+1)m1-(n1+1)m) Lm+m1,n+n1. In this paper, we determine the second cohomology group and the second Leibniz cohomology group of B.
Lie Symmetry Analysis of the Hopf Functional-Differential Equation
Daniel D. Janocha
2015-08-01
Full Text Available In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of Oberlack and Wacławczyk (2006, Arch. Mech. 58, 597, (2013, J. Math. Phys. 54, 072901, where the extended Lie symmetry analysis is performed in the Fourier space. Here, we introduce a method to perform the extended Lie symmetry analysis in the physical space where we have to deal with the transformation of the integration variable in the appearing integral terms. The method is based on the transformation of the product y(xdx appearing in the integral terms and applied to the functional formulation of the viscous Burgers equation. The extended Lie symmetry analysis furnishes all known symmetries of the viscous Burgers equation and is able to provide new symmetries associated with the Hopf formulation of the viscous Burgers equation. Hence, it can be employed as an important tool for applications in continuum mechanics.
Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups
Batat, Wafaa
2011-01-01
We classify Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups. All algebraic Ricci solitons that we obtain are sol-solitons. In particular, we prove that, contrary to the Riemannian case, Lorentzian Ricci solitons need not to be algebraic Ricci solitons.
Religiosity and Lie Scores: A Question of Interpretation.
Francis, Leslie J.; And Others
1988-01-01
Administered Francis scale of attitude towards Christianity and the Junior Eysenck Personality Questionnaire to 3,228 11- to 16-year-olds. Found positive relationship between religiosity and lie scale scores. Examined relationship in light of three theories that religious people are less mature, more socially conforming, or simply bigger liars.…
A CLINICAL STUDY OF OUTCOME OF LABOUR IN TRANSVERSE LIE
Vijayalakshmi
2015-08-01
Full Text Available Transverse lie complicates approximately 0.5% of birth and may result in neglected or impacted shoulder presentation leading to obstructed labour, rupture uterus and postpartum haemorrhage which may result in death of the mother, if not adequately managed in labour . A prospective observational study done in VI MS B ellary, Karnataka, aim of the study was to know the maternal and fetal outcome, to study caesarean rate, maternal and neonatal complications following caesarean. Objective of the study is to analyse the various modes of outcome of transverse lie to kno w the fetal and maternal mortality and morbidity , to improve the conditions which decreases these rates and guide us for better management of these cases. Out of 6116 deliveries100 cases were transverse lie during 2year period from April 1999 to January 20 01. Out of 100 cases , 76 were caesarean sections, 48 were live births, 7 were neonatal deaths, 45 were still births. Maternal morbidity was 2 cases required subtotal hysterectomy. There were no maternal deaths. Elective caesarean section should be advised in all booked cases with transverse lie at term, after ruling out congenital anomalies of the fetus by anomaly scan.
Invariants of solvable rigid Lie algebras up to dimension 8
Campoamor-Stursberg, Rutwig [Depto Geometria y Topologia, Fac. CC Matematicas UCM, Madrid (Spain)]. E-mail: rutwig@nfssrv.mat.ucm.es
2002-08-02
The invariants of all complex solvable rigid Lie algebras up to dimension 8 are computed. Moreover we show, for rank 1 solvable algebras, some criteria to deduce the non-existence of nontrivial invariants or the existence of fundamental sets of invariants formed by rational functions of the Casimir invariants of the associated nilradical. (author)
Evaluation of the Dutch subsurface geoportal: What lies beneath?
Lance, K.T.; Georgiadou, Y.; Bregt, A.K.
2011-01-01
This paper focuses on a geoportal from a “what lies beneath” perspective. It analyses processes of budgeting, planning, monitoring, performance measurement, and reporting of the national initiative titled Digital Information of the Dutch Subsurface (known by its Dutch acronym, DINO). The study is us
On Approximation of Lie Groups by Discrete Subgroups
Hatem Hamrouni; Salah Souissi
2014-02-01
A locally compact group is said to be approximated by discrete sub-groups (in the sense of Tôyama) if there is a sequence of discrete subgroups of that converges to in the Chabauty topology (or equivalently, in the Vietoris topology). The notion of approximation of Lie groups by discrete subgroups was introduced by Tôyama in Kodai Math. Sem. Rep. 1 (1949) 36–37 and investigated in detail by Kuranishi in Nagoya Math. J. 2 (1951) 63–71. It is known as a theorem of Tôyama that any connected Lie group approximated by discrete subgroups is nilpotent. The converse, in general, does not hold. For example, a connected simply connected nilpotent Lie group is approximated by discrete subgroups if and only if has a rational structure. On the other hand, if is a discrete uniform subgroup of a connected, simply connected nilpotent Lie group then is approximated by discrete subgroups $_n$ containing . The proof of the above result is by induction on the dimension of , and gives an algorithm for inductively determining $_n$. The purpose of this paper is to give another proof in which we present an explicit formula for the sequence $(_n)_{n≥ 0}$ in terms of . Several applications are given.
Climate-driven Sympatry does not Lead to Foraging Competition Between Adélie and Gentoo Penguins
Cimino, M. A.; Moline, M. A.; Fraser, W.; Patterson-Fraser, D.; Oliver, M. J.
2016-02-01
Climate-driven sympatry may lead to competition for food resources between species, population shifts and changes in ecosystem structure. Rapid warming in the West Antarctic Peninsula (WAP) is coincident with increasing gentoo penguin and decreasing Adélie penguin populations, suggesting that competition for food may exacerbate the Adélie penguin decline. At Palmer Station, we tested for foraging competition between these species by comparing their prey, Antarctic krill, distributions and penguin foraging behaviors on fine scales. To study these predator-prey dynamics, we simultaneously deployed penguin satellite transmitters, and a REMUS autonomous underwater vehicle that acoustically detected krill aggregations and measured physical and biological properties of the water column. We detected krill aggregations within the horizontal and vertical foraging ranges of Adélie and gentoo penguin. In the upper 100 m of the water column, the distribution of krill aggregations were mainly associated with CHL and light, suggesting that krill selected for habitats that balance the need to consume food and avoid predation. Adélie and gentoo penguins mainly had spatially segregated foraging areas but in areas of overlap, gentoo penguins switched foraging behavior by foraging at deeper depths, a strategy which limits competition with Adélie penguins. This suggests that climate-driven sympatry does not necessarily result in competitive exclusion. Contrary to a recent theory, which suggests that increased competition for krill is the major driver of Adélie penguin population declines, we suggest that declines in Adélie penguins along the WAP are more likely due to direct and indirect climate impacts on their life histories.
Sharova, A. S.; Maklygina, YU S.; Lisichkin, G. V.; Mingalev, P. G.; Loschenov, V. B.
2016-08-01
The spectroscopic properties of potentially perspective nanostructure: diamond nanoparticles with a surface layer of IR-photosensitizer, bacteriochlorin, were experimentally investigated in this study. Such specific structure of the object encourages enhancement of the drug tropism to the tumor, as well as increasing of photodynamic penetration depth. The size distribution spectra of diamond nanoparticles; diamond nanoparticles, artificially covered with bacteriochlorin molecules layer, in aqueous solution, were obtained during the study. Based on the absorption and fluorescence spectra analysis, the benefits of functional nanostructure as a drug for deep-lying tumor diagnostics and therapy were reviewed.
Lie group analysis method for two classes of fractional partial differential equations
Chen, Cheng; Jiang, Yao-Lin
2015-09-01
In this paper we deal with two classes of fractional partial differential equation: n order linear fractional partial differential equation and nonlinear fractional reaction diffusion convection equation, by using the Lie group analysis method. The infinitesimal generators general formula of n order linear fractional partial differential equation is obtained. For nonlinear fractional reaction diffusion convection equation, the properties of their infinitesimal generators are considered. The four special cases are exhaustively investigated respectively. At the same time some examples of the corresponding case are also given. So it is very convenient to solve the infinitesimal generator of some fractional partial differential equation.
Some exact solutions for a unidimensional fokker-planck equation by using lie symmetries
Hugo Hernán Ortíz-Álvarez
2015-01-01
Full Text Available The Fokker Planck equation appears in the study of diffusion phenomena, stochastics processes and quantum and classical mechanics. A particular case fromthis equation, ut − uxx − xux − u=0, is examined by the Lie group method approach. From the invariant condition it was possible to obtain the infinitesimal generators or vectors associated to this equation, identifying the corresponding symmetry groups. Exact solution were found for each one of this generators and new solution were constructed by using symmetry properties.
Piele, Philip K.
Chapter 7 of a book on school law, this chapter deals with 1979 cases involving disputes over property. Cases involving taxpayer attempts to prevent the construction of school buildings dominate this year's property chapter, as they did last year's. Yet, paradoxically, there is also a significant increase in cases in which taxpayers tried to…
Kozlov, I K [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2014-04-30
In this paper we study topological properties of an integrable case for Euler's equations on the Lie algebra so(4), which can be regarded as an analogue of the classical Kovalevskaya case in rigid body dynamics. In particular, for all values of the parameters of the system under consideration, the bifurcation diagrams of the momentum mapping are constructed, the types of critical points of rank 0 are determined, the bifurcations of Liouville tori are described, and the loop molecules are computed for all singular points of the bifurcation diagrams. It follows from the obtained results that some topological properties of the classical Kovalevskaya case can be obtained from the corresponding properties of the considered integrable case on the Lie algebra so(4) by taking a natural limit. Bibliography: 21 titles.
儿童谎言的两种不同类型：白谎与黑谎%Two different types of children lie:black lie and white lie
张娜
2014-01-01
According to the motivation lies, lies can bedivided into black lie and white lie, white lie is said to avoid hurting others or please others lie, to be altruistic lies. Black lie is to conceal the error or avoid own negligence punished told lies, is the selfish. Adult should break on children'slying lump together ideas, black lie and white lie differently from children.%依据谎言的动机，可将谎言划分为白谎与黑谎，白谎是为避免伤害他人或取悦他人而说的假话，是利他性谎言。黑谎是为隐瞒错误或避免自身的过失受到惩罚而说的假话，是利己性谎言。成人应打破对儿童说谎一概而论的观念，区别对待儿童的白谎与黑谎。
Lie Symmetrical Non-Noether Conserved Quantities of Poincaré-Chetaev Equations
ZHANG Peng-Yu; FANG Jian-Hui
2005-01-01
In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré-Chetaev equations under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced.
Children's Categorization and Evaluation of Different Types of Lies and Truths.
Bussey, Kay
1999-01-01
Investigated 4-, 8-, and 11-year-olds' ability to categorize intentionally false and true statements as lies and truths. Found that older children were more likely to categorize false statements as lies and true statements as truths than were 4-year-olds. Antisocial lies were rated as most serious, and "white lies" as least serious. Anticipated…
Being honest about dishonesty: correlating self-reports and actual lying
Halevy, R.; Shalvi, S.; Verschuere, B.
2014-01-01
Does everybody lie? A dominant view is that lying is part of everyday social interaction. Recent research, however, has claimed, that robust individual differences exist, with most people reporting that they do not lie, and only a small minority reporting very frequent lying. In this study, we found
The Concept of Lying in Adolescents and Young Adults: Testing Sweetser's Folkloristic Model.
Lee, Kang; Ross, Hollie J.
1997-01-01
Tested E. E. Sweetser's (1987) model of lying, which emphasizes critical contribution of social factors to definitions of lie. Presented vignettes to 12-, 16-, and 19-year olds--half with prototypic lie-telling, half with truth-telling--and asked them to indicate degree of agreement that statement was a lie. Found that effects of age, help-harm…
Average Exceptional Lie Group Hierarchy and High Energy Physics
El Naschie, M S
2008-01-01
Starting from an invariant total dimension for an exceptional Lie symmetry groups hierarchy, we drive all the essential characteristic and coupling constants of the fundamental interactions of physics. It is shown in a most simplistic fashion that all physical fields are various transfinite scaling transformation and topological deformation of each other. An extended standard model on the other hand turned out to be a compact sub group H of a version of E7 exceptional Lie group E7(−5) with dimH =69. Thus particle physics, electromagnetism as well as gravity and the bulk are all representable via modular spaces akin to the famous compactified version of F. Klein’s modular curve.
Noether and Lie symmetries for charged perfect fluids
Kweyama, M C; Maharaj, S D
2013-01-01
We study the underlying nonlinear partial differential equation that governs the behaviour of spherically symmetric charged fluids in general relativity. We investigate the conditions for the equation to admit a first integral or be reduced to quadratures using symmetry methods for differential equations. A general Noether first integral is found. We also undertake a comprehensive group analysis of the underlying equation using Lie point symmetries. The existence of a Lie symmetry is subject to solving an integro-differential equation in general; we investigate the conditions under which it can be reduced to quadratures. Earlier results for uncharged fluids and particular first integrals for charged matter are regained as special cases of our treatment.
Lie transform Hamiltonian perturbation theory for limit cycle systems
Shah, Tirth; Chakraborty, Sagar
2016-01-01
Usage of a Hamiltonian perturbation theory for nonconservative system is counterintuitive and in general, a technical impossibility by definition. However, the dual (time independent) Hamiltonian formalism for nonconservative systems have opened the door for using various Hamiltonian (and hence, Lagrangian) perturbation theories for investigating the dynamics of such systems. Following the recent extension of the canonical perturbation theory that brings Li\\'enard systems possessing limit cycles under its scope, here we show that the Lie transform Hamiltonian perturbation theory can also be generalized to find perturbative solutions for similar systems. The Lie transform perturbation theories are comparatively easier while seeking higher order corrections in the perturbative series for the solutions and they are also numerically implementable using any symbolic algebra package. For the sake of concreteness, we have illustrated the methodology using the important example of the van der Pol oscillator. While th...
Lie symmetries of semi-linear Schroedinger equations and applications
Stoimenov, Stoimen [Laboratoire de Physique des Materiaux (CNRS UMR 7556), Universite Henri Poincare Nancy I, B.P.239, F-54506 Vandoeuvre les Nancy Cedex (France); Henkel, Malte [Laboratoire de Physique des Materiaux (CNRS UMR 7556), Universite Henri Poincare Nancy I, B.P.239, F-54506 Vandoeuvre les Nancy Cedex (France)
2006-05-15
Conditional Lie symmetries of semi-linear 1D Schroedinger and diffusion equations are studied in case the mass (or the diffusion constant) is considered as an additional variable and/or where the couplings of the non-linear part have a non-vanishing scaling dimension. In this way, dynamical symmetries of semi-linear Schroedinger equations become related to certain subalgebras of a three-dimensional conformal Lie algebra (conf{sub 3}){sub C}. The representations of these subalgebras are classified and the complete list of conditionally invariant semi-linear Schroedinger equations is obtained. Applications to the phase-ordering kinetics of simple magnets and to simple particle-reaction models are briefly discussed.
Spinor Lie derivatives and Fermion stress-energies
Helfer, Adam D
2016-01-01
Stress-energies for Fermi fields are derived from the principle of general covariance. This is done by developing a notion of Lie derivatives of spinors along arbitrary vector fields. A substantial theory of such derivatives was first introduced by Kosmann; here I show how an apparent conflict in the literature on this is due to a difference in the definitions of spinors, and that tracking the Lie derivative of the Infeld-van der Waerden symbol, as well as the spinor fields under consideration, gives a fuller picture of the geometry and leads to the Fermion stress-energy. The differences in the definitions of spinors do not affect the results here, but could matter in certain quantum-gravity programs and for spinor transformations under discrete symmetries.
Lie algebras for some specific dissipative Landau–Zener problems
Kenmoe, M.B. [Mesoscopic and Multilayer Structures Laboratory (MMSL), Faculty of Science, Department of Physics, University of Dschang (Cameroon); Mkam Tchouobiap, S.E., E-mail: esmkam@yahoo.com [Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Sciences, University of Buea, PO Box 63, Buea (Cameroon); Danga, J.E.; Kenfack Sadem, C.; Fai, L.C. [Mesoscopic and Multilayer Structures Laboratory (MMSL), Faculty of Science, Department of Physics, University of Dschang (Cameroon)
2015-03-20
We demonstrate that some specific problems of Landau–Zener transitions in a qubit coupled to an environment (problems designed as dissipative) can be matched onto the frame of the original problem without dissipation, providing an appropriate Lie algebra. Focusing on the origin of quantum noises, the cases of bosonic and spin baths are considered and presented. Finally, making use of the algebra framework, the logic is shown in action for respectively two important additional quantum models, namely the Jaynes–Cummings and an isolated double quantum dots models. - Highlights: • A finite temperature result for dissipative Landau–Zener transitions in a qubit coupled to an environment is proposed. • The quantum noises for bosonic and spin baths are considered. • Lie algebras reduction method coupled to the separation method and the fast driving approximation is proposed. • Jaynes–Cummings and a double quantum dots models are studied as illustrations of the algebra.
Random Lie group actions on compact manifolds: a perturbative analysis
Sadel, Christian
2008-01-01
A random Lie group action on a compact manifold generates a discrete time Markov process. The main object of this paper is the evaluation of associated Birkhoff sums in a regime of weak, but sufficiently effective coupling of the randomness. This effectiveness is expressed in terms of random Lie algebra elements and replaces the transience or Furstenberg's irreducibility hypothesis in related problems. The Birkhoff sum of any given smooth function then turns out to be equal to its integral w.r.t. a unique smooth measure on the manifold up to errors of the order of the coupling constant. Applications to the theory of products of random matrices and a model of a disordered quantum wire are presented.
On the low lying singlet states of BeO
Bauschlicher, C. W., Jr.; Lengsfield, B. H.; Yarkony, D. R.
1980-01-01
Calculations of the ground and low-lying singlet states of BeO are performed in order to gain an understanding of the techniques needed to treat the excited states of other, more complex, ionic molecules. The MCSCF and CI calculations are based on a Gaussian basis set of slightly better than double zeta plus polarization quality for single configuration descriptions of the states. The calculated X-A and X-B state separations are found to be in agreement with experimental measurements. The 1 Sigma - and 1 Delta states are predicted to lie approximately 40,000 kaysers above the ground state and are identified as the C and D states.The 2 1 Pi state is found to be approximately 15,000 kaysers and the 3 1 Sigma + state is found to be approximately 65,000 kaysers above the ground state.
Coadjoint orbits of reductive type of seaweed Lie algebras
Moreau, Anne
2011-01-01
A connected algebraic group Q defined over a field of characteristic zero is quasi-reductive if there is an element of its dual of reductive type, that is such that the quotient of its stabiliser by the centre of Q is a reductive subgroup of GL(q), where q=Lie(Q). Due to results of M. Duflo, coadjoint representation of a quasi-reductive Q possesses a so called maximal reductive stabiliser and knowing this subgroup, defined up to a conjugation in Q, one can describe all coadjoint orbits of reductive type. In this paper, we consider quasi-reductive parabolic subalgebras of simple complex Lie algebras as well as all seaweed subalgebras of gl(n) and describe the classes of their maximal reductive stabilisers.
Classification of real low-dimensional Jacobi (generalized)-Lie bialgebras
Rezaei-Aghdam, A.; Sephid, M.
2017-09-01
We describe the definition of Jacobi (generalized)-Lie bialgebras ((g,ϕ0), (g∗,X 0)) in terms of structure constants of the Lie algebras g and g∗ and components of their 1-cocycles X0 ∈g and ϕ0 ∈g∗ in the basis of the Lie algebras. Then, using adjoint representations and automorphism Lie groups of Lie algebras, we give a method for classification of real low-dimensional Jacobi-Lie bialgebras. In this way, we obtain and classify real two- and three-dimensional Jacobi-Lie bialgebras.
Lie group analysis for multi-scale plasma dynamics
Kovalev, Vladimir F
2011-01-01
An application of approximate transformation groups to study dynamics of a system with distinct time scales is discussed. The utilization of the Krylov-Bogoliubov-Mitropolsky method of averaging to find solutions of the Lie equations is considered. Physical illustrations from the plasma kinetic theory demonstrate the potentialities of the suggested approach. Several examples of invariant solutions for the system of the Vlasov-Maxwell equations for the two-component (electron-ion) plasma are presented.
On the linearization theorem for proper Lie groupoids
Crainic, Marius
2011-01-01
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zung's theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passing to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise conditions needed for the theorem to hold (which often have been misstated in the literature).
On the string topology category of compact Lie groups
2013-01-01
This paper examines the string topology category of a manifold, defined by Blumberg, Cohen and Teleman. Since the string topology category is a subcategory of a compactly generated triangulated category, the machinery of stratification, constructed by Benson, Krause and Iyengar, can be applied in order to gain an understanding of the string topology category. It is shown that an appropriate stratification holds when the manifold in question is a simply connected compact Lie group. This last r...
Lie Symmetries and Criticality of Semilinear Differential Systems
Yuri Bozhkov
2007-03-01
Full Text Available We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers.
The Demazure-Tits subgroup of a simple Lie group
Michel, L.; Patera, J.; Sharp, R. T.
1988-04-01
The Demazure-Tits subgroup of a simple Lie group G is the group of invariance of Clebsch-Gordan coefficients tables (assuming an appropriate choice of basis). The structure of the Demazure-Tits subgroups of An, Bn, Cn, Dn, and G2 is described. Orbits of the permutation action of the DT group in any irreducible finite-dimensional representation space of A2, C2, and G2 are decomposed into the sum of irreducible representations of the DT group.
无
2004-01-01
@@ Should doctors ever lie to benefit their patient-to speed recovery or to conceal the approach of death? In medicine as in law, government, and other lines of work,the requirements of honesty often seem dwarfed (变矮小)by greater needs: the need to shelter from brutal news or to uphold a promise of secrecy; to expose corruption or to promote the public interest.
Geometry Algorisms of Dynkin Diagrams in Lie Group Machine Learning
Huan Xu; Fanzhang Li
2006-01-01
This paper uses the geometric method to describe Lie group machine learning (LML)based on the theoretical framework of LML, which gives the geometric algorithms of Dynkin diagrams in LML. It includes the basic conceptions of Dynkin diagrams in LML ,the classification theorems of Dynkin diagrams in LML, the classification algorithm of Dynkin diagrams in LML and the verification of the classification algorithm with experimental results.
AUTOMRPPHISM GROUP OF LIE ALGEBRA C(t)d/dt
DU HONG
2003-01-01
The Lie algebra of derivations of rational function field C(t) is C(t)d/dt. The automorphism group of C(t) is well known as to be isomorphic to the projective linear group PGL(2, C). In this short note we prove that every automorphism of C(t)d/dt can be induced in a natural way from an automorphism of C(t).
Consistent deniable lying : privacy in mobile social networks
Belle, Sebastian Kay; Waldvogel, Marcel
2008-01-01
Social networking is moving to mobile phones. This not only means continuous access, but also allows to link virtual and physical neighbourhood in novel ways. To make such systems useful, personal data such as lists of friends and interests need to be shared with more and frequently unknown people, posing a risk to your privacy. In this paper, we present our approach to social networking, Consistent Deniable Lying (CDL). Using easy-to-understand mechanisms and tuned to this environment, i...
Analysis on singular spaces: Lie manifolds and operator algebras
Nistor, Victor
2016-07-01
We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16-21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds-called "Lie manifolds" -that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here-work that spans over close to two decades-was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.
Adjoint representation of the graded Lie algebra osp(2/1; C) and its exponentiation
Ilyenko, K
2003-01-01
We construct explicitly the grade star Hermitian adjoint representation of osp(2/1; C) graded Lie algebra. Its proper Lie subalgebra, the even part of the graded Lie algebra osp(2/1; C), is given by su(2) compact Lie algebra. The Baker-Campbell-Hausdorff formula is considered and reality conditions for the Grassman-odd transformation parameters, which multiply the pair of odd generators of the graded Lie algebra, are clarified.
Co-splitting of Simple Lie Algebras of Typ e A, D, E
Zhao Yu-e; Du Xian-kun
2015-01-01
In this paper, through a meticulous description of finite root system, a concrete comultiplication with an explicit action on the basis elements of finite dimensional simple Lie algebras of type A, D, E is constructed. Then any finite dimensional simple Lie algebra of type A, D, E is endowed with a new generalized Lie coalgebra splitting. This construction verifies the known existence of a co-split Lie structure on any finite dimensional complex simple Lie algebra.
Terzis, Petros A
2010-01-01
Lie group symmetry analysis for systems of coupled, nonlinear ordinary differential equations is performed in order to obtain the entire solution space to Einstein's field equations for vacuum Bianchi spacetime geometries. The symmetries used are the automorphisms of the Lie algebra of the corresponding three- dimensional isometry group acting on the hyper-surfaces of simultaneity for each Bianchi Type, as well as the scaling and the time reparametrization symmetry. The method is applied to Bianchi Types I; II; IV and V. The result is the acquisition, in each case, of the entire solution space of either Lorenzian of Euclidean signature. This includes all the known solutions for each Type and the general solution of Type IV (in terms of sixth Painlev\\'e transcendent PVI).
The Hall Nilpotentce Rule of Lie Rings%Lie 环的Hall幂零性准则
杨艳
2007-01-01
首先仿照幂零群的处理方式,引进幂零Lie环的下中心列,并给出Lie 环的下中心列商群与Lab的张量积的关系,最后根据群上的Hall幂零性准则,给出了Lie环的Hall幂零性准则,并予以证明.
Verschuere, Bruno; in ´t Hout, Willem
2016-01-01
The cognitive view on deception holds that lying typically requires additional mental effort as compared to truth telling. Psychopathy, however, has been associated with swift and even compulsive lying, leading us to explore the ease and compulsive nature of lying in psychopathic offenders. We explored the costs of instructed lying versus truth telling through RTs and error rates in 52 violent male offenders, who were assessed with the Youth Psychopathic Traits Inventory (YPI). Our deception paradigm also included trials with the free choice to lie or tell the truth. By coupling monetary loss to slow and erroneous responding, we hypothesized that the frequency of lying despite likely negative consequences, would provide an index of compulsive lying. Offenders were slower and erred more often when lying than when telling the truth, and there was no robust association between psychopathy and the cognitive cost of lying. From an applied perspective, this suggests that psychopathy may not threaten the validity of computerized cognition-based lie detection. In the face of probable negative consequences, high grandiose-manipulative offenders chose to lie three times as often as low grandiose-manipulative offenders. Our new lying frequency index is a first attempt to create a much needed tool to empirically examine compulsive lying, and provides preliminary support for the compulsive nature of lying in grandiose-manipulative offenders. Alternative interpretation of the findings are discussed. PMID:27391854
Microscopic study of low-lying collectivebands in 77Kr
K C Tripathy; R Sahu; S Mishra
2006-02-01
The structure of the collective bands in 77Kr is investigated within our deformed shell model (DSM) based on Hartree-Fock states. The different levels are classified into collective bands on the basis of their (2) values. The calculated = 5/2+ ground band agrees reasonably well with the experiment. An attempt has been made to study the structure of the 3-quasiparticle band based on large state in this nucleus. The calculated collective bands, the (2), and (1) values are compared with available experimental data. The nature of alignments in the low-lying bands is also analyzed.
Representations of centrally extended Lie superalgebra psl(2|2)
Matsumoto, Takuya, E-mail: t.matsumoto@uu.nl [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3854 CE Utrecht (Netherlands); Molev, Alexander, E-mail: alexander.molev@sydney.edu.au [School of Mathematics and Statistics, University of Sydney, NSW 2006 (Australia)
2014-09-15
The symmetries provided by representations of the centrally extended Lie superalgebra psl(2|2) are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory correspondence and one-dimensional Hubbard model. We give a complete description of finite-dimensional irreducible representations of this superalgebra thus extending the work of Beisert which deals with a generic family of representations. Our description includes a new class of modules with degenerate eigenvalues of the central elements. Moreover, we construct explicit bases in all irreducible representations by applying the techniques of Mickelsson–Zhelobenko algebras.
Surfaces immersed in Lie algebras associated with elliptic integrals
Grundland, A M; Post, S, E-mail: grundlan@crm.umontreal.ca, E-mail: post@crm.umontreal.ca [Centre de Recherches Mathematiques, Universite de Montreal, Montreal CP6128, QC H3C 3J7 (Canada)
2012-01-13
The objective of this work is to adapt the Fokas-Gel'fand immersion formula to ordinary differential equations written in the Lax representation. The formalism of generalized vector fields and their prolongation structure is employed to establish necessary and sufficient conditions for the existence and integration of immersion functions for surfaces in Lie algebras. As an example, a class of second-order, integrable, ordinary differential equations is considered and the most general solutions for the wavefunctions of the linear spectral problem are found. Several explicit examples of surfaces associated with Jacobian and P-Weierstrass elliptic functions are presented. (paper)
ENDOMORPHISMS OF LIE ALGEBRA F[t]d/dt
DU Hong
2004-01-01
Let F be a field of characteristic zeroWn =F[t +1/1,t +1/2,…,t +1/n]а/аt1+ are simple infinite dimensional Lie algebraIn Zhao's paper, it was conjectured thatEnd(W,n+) - {0} = Aut(Wn+) and it was proved that the validity of this conjecture im-plies the validity of the well-known Jacobian conjectureIn this short note, we check theconjecture above for n = 1We show End(W+1) - {0} = Aut(W1+).
Shipbuilding power lies in high-end market
2011-01-01
The 2011 edition of Guideline Index for Readjusting Industrial Structure issued by the National Development and Reform Commission underlines the construction of high-end ships and the upgrading of shipbuilding technology.This shows that ifChina's shipbuilding industry is to become powerful,it should go all out to open up the fields of high-end ship construction so that the industry may have a greater share in the world market.Therefore,the power of our shipbuilding industry lies in the high-end market.
Quantum stochastic calculus and representations of Lie superalgebras
Eyre, Timothy M W
1998-01-01
This book describes the representations of Lie superalgebras that are yielded by a graded version of Hudson-Parthasarathy quantum stochastic calculus. Quantum stochastic calculus and grading theory are given concise introductions, extending readership to mathematicians and physicists with a basic knowledge of algebra and infinite-dimensional Hilbert spaces. The develpment of an explicit formula for the chaotic expansion of a polynomial of quantum stochastic integrals is particularly interesting. The book aims to provide a self-contained exposition of what is known about Z_2-graded quantum stochastic calculus and to provide a framework for future research into this new and fertile area.
Lie groups, differential equations, and geometry advances and surveys
2017-01-01
This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.
Competitive Pressure and Job Interview Lying: A Game Theoretical Analysis
Midjord, Rune
2012-01-01
We consider a job contest in which candidates go through interviews (cheap talk) and are subject to reference checks. We show how competitive pressure - increasing the ratio of "good" to "bad" type candi- dates - can lead to a vast increase in lying and in some cases make bad hires more likely. As the number of candidates increases, it becomes harder to in- duce truth-telling. The interview stage becomes redundant if the candidates, a priori, know each others' type or the result of their own ...
Noncollisional excitation of low-lying states in gaseous nebulae
Rubin, Robert H.
1986-01-01
Consideration is given to the effects of processes other than electron collisional excitation on the energy level populations of species of C, N, and O. It is found that dielectronic as well as direct-radiative recombination may contribute significantly and in some cases be the major input to populating the low-lying metastable levels. It is concluded that the most pronounced changes occur when there is a large effective recombination coefficient to a level and when T(e) is low. The most dramatic change among the forbidden lines occurs for the O II forbidden lines.
Lie Particle And Its Batalin-Tyutin Extension
Ghosh, S; Ghosh, Subir; Pal, Probir
2006-01-01
In this Letter we have proposed a point particle model that generates a noncommutative three-space, with the coordinate brackets being Lie algebraic in nature. The work is in the spirit of our earlier works in this connection, i.e., PLB 618 (2005)243 and PLB 623 (2005)251. This non-linear and operatorial nature of the configuration space coordinate algebra can pose problems regarding its quantization. This prompts us to embed the model in the Batalin-Tyutin extended space where the equivalent model comprises of phase space variables satisfying a canonical algebra.
Low lying charmonium states at the physical point
Mohler, Daniel; Kronfeld, Andreas S; Lee, Song-haeng; Levkova, Ludmila; Simone, J N
2014-01-01
We present results for the mass splittings of low-lying charmonium states from a calculation with Wilson clover valence quarks with the Fermilab interpretation on an asqtad sea. We use five lattice spacings and two values of the light sea quark mass to extrapolate our results to the physical point. Sources of systematic uncertainty in our calculation are discussed and we compare our results for the 1S hyperfine splitting, the 1P-1S splitting and the P-wave spin orbit and tensor splittings to experiment.
Different Connotations of "Modesty" Lying in Western and Eastern Culture
涂艳
2015-01-01
as a common morality,politeness is the symbol of human civilization and a primary principle abided by people in interpersonal communication.However,the standard and the way of expression of politeness are fluctuated with different culture.This essay takes analysis on different connotations of"modesty" lying in the western culture and eastern culture deeply and explains the cause for that,for the purpose of helping people avoid pragmatic mistake in intercultural communication at the best to achieve considerable communicative effect.
Lie algebra type noncommutative phase spaces are Hopf algebroids
Meljanac, Stjepan; Škoda, Zoran; Stojić, Martina
2016-11-01
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way; therefore, obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here, we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.
Lie algebra type noncommutative phase spaces are Hopf algebroids
Meljanac, Stjepan
2014-01-01
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way, therefore obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.
Generalized Lotka—Volterra systems connected with simple Lie algebras
Charalambides, Stelios A.; Damianou, Pantelis A.; Evripidou, Charalambos A.
2015-06-01
We devise a new method for producing Hamiltonian systems by constructing the corresponding Lax pairs. This is achieved by considering a larger subset of the positive roots than the simple roots of the root system of a simple Lie algebra. We classify all subsets of the positive roots of the root system of type An for which the corresponding Hamiltonian systems are transformed, via a simple change of variables, to Lotka-Volterra systems. For some special cases of subsets of the positive roots of the root system of type An, we produce new integrable Hamiltonian systems.
GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS
陈正新
2014-01-01
Let P be a parabolic subalgebra of a general linear Lie algebra gl(n, F) over a field F, where n ≥ 3, F contains at least n different elements, and char(F) 6= 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation.
International Workshop "Groups, Rings, Lie and Hopf Algebras"
2003-01-01
The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.
Low-lying quadrupole collectivity in {sup 136}Xe
Stahl, Christian; Leske, Joerg; Pietralla, Norbert; Reese, Michael [Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany); Bazzacco, Dino; Farnea, Enrico [Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padova (Italy); Gadea, Andres [Instituto de Fisica Corpuscular, CSIC-Universitat de Valencia, Valencia (Spain); Gottardo, Andrea [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, Legnaro (Italy); Dipartimento di Fisica e Astronomia dell' Universita degli Studi di Padova, Padova (Italy); John, Philipp Rudolf; Michelagnoli, Caterina [Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Padova (Italy); Dipartimento di Fisica e Astronomia dell' Universita degli Studi di Padova, Padova (Italy); Valiente-Dobon, Jose Javier [Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, Legnaro (Italy)
2015-07-01
We present recent results from our investigation of low-lying quadrupole collectivity in the semi-magic N=82 nucleus {sup 136}Xe. An experiment was performed at the Legnaro National Laboratory employing the AGATA demonstrator. Level-lifetimes and B(E2, 0{sup +}{sub 1}→2{sup +}{sub i})-values were determined from Coulomb excitation and by the continuous-angle DSA method exploiting AGATA's position resolution. 2{sup +}{sub i} - states up to i=7 were excited and analyzed.
Functional Group Chemistry (by James R. Hanson)
Karty, Joel M.
2002-06-01
Given its density and brevity and the apparent requirement of previous organic chemistry knowledge, Functional Group Chemistry is inappropriate as a stand-alone text for first-year organic students. It is also difficult to imagine using it as a supplement to a traditional textbook, since the textbook would presumably provide the same material in greater depth and with better clarity. The end-of-chapter problems in Functional Group Chemistry, however, would provide excellent exam and supplemental homework questions, and would be appropriate given the greater emphasis on reaction mechanisms in the traditional textbook. Perhaps the best use for Functional Group Chemistry, then, is for students returning after having had a year of organic chemistry, either for a quick reference, or for an in-depth review in studying for a standardized exam.
Annus ei taha olla esirikas / Martin Hanson
Hanson, Martin, 1984-
2006-01-01
Ilmunud ka: Delovõje Vedomosti 18. okt. lk. 2-3. Merko Grupp AS-i omaniku Toomas Annuse äritegevusest, suhtlemisest meediaga. Toomas Annuse CV, osalused firmades. Vt. samas intervjuud Toomas Annusega
Kuu artist Hedvig Hanson. Kuula / Mart Juur
Juur, Mart, 1964-
2008-01-01
Intervjuu laulja Hedvig Hansoniga heliplaadist "Kohtumistund". Heliplaatidest: Anastacia "Heavy Rotation", Snow Patrol "A Hundred Million Suns", James Morrison "Songs for You, Truths for Me", Ry Cooder "The Ry Cooder Anthology: The UFO Has Landed", Seal "Soul", Tracy Chapman "Our Bright Future", Sophia Somajo "The Laptop Diaries"
Kuu artist Hedvig Hanson. Kuula / Mart Juur
Juur, Mart, 1964-
2008-01-01
Intervjuu laulja Hedvig Hansoniga heliplaadist "Kohtumistund". Heliplaatidest: Anastacia "Heavy Rotation", Snow Patrol "A Hundred Million Suns", James Morrison "Songs for You, Truths for Me", Ry Cooder "The Ry Cooder Anthology: The UFO Has Landed", Seal "Soul", Tracy Chapman "Our Bright Future", Sophia Somajo "The Laptop Diaries"
BSA : Eestis lokkab piraattarkvara kasutus / Martin Hanson
Hanson, Martin, 1984-
2008-01-01
Ilmunud ka: Delovõje Vedomosti 13. veebr. lk. 24. Piraattarkvara vastu võitleva ülemaailmse organisatsiooni BSA uuringu järgi on 52% Eestis kasutatavast tarkvarast piraattarkvara. Diagramm: Piraattarkvara levik. Kommenteerivad Rain Laane, Sulev Sisask ja riigikogu liige Hannes Astok. Ajal. Delovõje Vedomosti Hannes Astoki kommentaari asemel Andrei Sokolovi kommentaar
Lavastuses liitub tants animatsiooniga / Raimu Hanson
Hanson, Raimu, 1957-
2004-01-01
7. veebr. esietendub Vanemuises tantsulavastus "Alice imedemaal". Etendus põhineb briti kirjaniku L. Carrolli samanimelisel lasteraamatul, koreograaf M. Murdmaa, kunstnik K. Jancis ja muusika on kirjutanud ungari helilooja S. Kall̤s, Alice'i osa tantsib korealanna Hye Min Kim
Kõrge majandusauhind Mart Laarile / Martin Hanson
Hanson, Martin, 1984-
2006-01-01
Cato instituut premeeris Mart Laari majandusteadlase Milton Friedmani nimelise auhinnaga ja üle 6 miljoni krooniga. Vt. samas: Mart Laari varasemad autasud; Milton Friedmani auhind anti kätte kolmandat korda. Kommenteerivad: Ivari Padar, Tiit Vähi, Tiit Tammsaar, Linnar Viik ja Andres Lipstok
Kinoonud linastavad muusikalise armuloo / Raimu Hanson
Hanson, Raimu, 1957-
2010-01-01
Tartu ülikooli doktorant Martin Liira juhib koos Urmas Reisbergi ja Richard Meiterniga klubilaadse noorteühenduse Kinoonud tegevust. Äsja valmis ühenduse neljas film "Tudengimuusikal", autor Elo Madisson Tartu ülikoolist, peaosades on Adeele Sepp ja Dmitri Kurilov Viljandi Kultuuriakadeemiast
Kõrge majandusauhind Mart Laarile / Martin Hanson
Hanson, Martin, 1984-
2006-01-01
Cato instituut premeeris Mart Laari majandusteadlase Milton Friedmani nimelise auhinnaga ja üle 6 miljoni krooniga. Vt. samas: Mart Laari varasemad autasud; Milton Friedmani auhind anti kätte kolmandat korda. Kommenteerivad: Ivari Padar, Tiit Vähi, Tiit Tammsaar, Linnar Viik ja Andres Lipstok
Deformation Quantization of Poisson Structures Associated to Lie Algebroids
Nikolai Neumaier
2009-09-01
Full Text Available In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E*, where E → M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even symplectic, our construction gets along without Kontsevich's formality theorem but is based on a generalized Fedosov construction. As the whole construction merely uses geometric structures of E we also succeed in determining the dependence of the resulting star products on these data in finding appropriate equivalence transformations between them. Finally, the concreteness of the construction allows to obtain explicit formulas even for a wide class of derivations and self-equivalences of the products. Moreover, we can show that some of our products are in direct relation to the universal enveloping algebra associated to the Lie algebroid. Finally, we show that for a certain class of star products on E* the integration with respect to a density with vanishing modular vector field defines a trace functional.
Lie algebra lattices and strings on T-folds
Satoh, Yuji; Sugawara, Yuji
2017-02-01
We study the world-sheet conformal field theories for T-folds systematically based on the Lie algebra lattices representing the momenta of strings. The fixed point condition required for the T-duality twist restricts the possible Lie algebras. When the T-duality acts as a simple chiral reflection, one is left with the four cases, A 1 , D 2 r , E 7 , E 8, among the simple simply-laced algebras. From the corresponding Englert-Neveu lattices, we construct the modular invariant partition functions for the T-fold CFTs in bosonic string theory. Similar construction is possible also by using Euclidean even self-dual lattices. We then apply our formulation to the T-folds in the E 8 × E 8 heterotic string theory. Incorporating non-trivial phases for the T-duality twist, we obtain, as simple examples, a class of modular invariant partition functions parametrized by three integers. Our construction includes the cases which are not reduced to the free fermion construction.
Lie algebra lattices and strings on T-folds
Satoh, Yuji
2016-01-01
We study the world-sheet conformal field theories for T-folds systematically based on the Lie algebra lattices representing the momenta of strings. The fixed point condition required for the T-duality twist restricts the possible Lie algebras. When the T-duality acts as a simple chiral reflection, one is left with the four cases, $A_1, D_{2r}, E_7, E_8$, among the simple simply-laced algebras. From the corresponding Englert-Neveu lattices, we construct the modular invariant partition functions for the T-fold CFTs in bosonic string theory. Similar construction is possible also by using Euclidean even self-dual lattices. We then apply our formulation to the T-folds in the $E_8 \\times E_8$ heterotic string theory. Incorporating non-trivial phases for the T-duality twist, we obtain, as simple examples, a class of modular invariant partition functions parametrized by three integers. Our construction includes the cases which are not reduced to the free fermion construction.
Some Results on Metric n-Lie Algebras
Rui Pu BAI; Wan Qing WU; Zhen Heng LI
2012-01-01
We study the structure of a metric n-Lie algebra G over the complex field C.Let (G) =S(+)R be the Levi decomposition,where R is the radical of (G) and S is a strong semisimple subalgebra of (G).Denote by m((G)) the number of all minimal ideals of an indecomposable metric n-Lie algebra and R⊥the orthogonal complement of R.We obtain the following results.As S-modules,R⊥ is isomorphic to the dual module of (G)/R.The dimension of the vector space spanned by all nondegenerate invariant symmetric bilinear forms on (G) is equal to that of the vector space of certain linear transformations on (G); this dimension is greater than or equal to m((G)) + 1.The centralizer of R in (G) is equal to the sum of all minimal ideals; it is the direct sum of R⊥ and the center of (G).Finally,(G) has no strong semisimple ideals if and only if R⊥ (C) R.
An index formula for perturbed Dirac operators on Lie manifolds
Carvalho, Catarina
2011-01-01
We give an index formula for a class of Dirac operators coupled with unbounded potentials. More precisely, we study operators of the form P := D+ V, where D is a Dirac operators and V is an unbounded potential at infinity on a possibly non-compact manifold M_0. We assume that M_0 is a Lie manifold with compactification denoted M. Examples of Lie manifolds are provided by asymptotically Euclidean or asymptotically hyperbolic spaces. The potential V is required to be invertible outside a compact set K and V^{-1} extends to a smooth function on M\\K that vanishes on all faces of M in a controlled way. Using tools from analysis on non-compact Riemannian manifolds, we show that the computation of the index of P reduces to the computation of the index of an elliptic pseudodifferential operator of order zero on M_0 that is a multiplication operator at infinity. The index formula for P can then be obtained from earlier results. The proof also yields similar index formulas for Callias-type pseudodifferential operators ...
Low-lying dipole strengths of {sup 50}Cr
Pai, H.; Beck, T.; Beller, J.; Gayer, U.; Mertes, L.; Pietralla, N.; Ries, P.; Romig, C.; Werner, V.; Zweidinger, M. [Institut fuer Kernphysik, Technische Universitaet Darmstadt, 64289 Darmstadt (Germany)
2015-07-01
Low-lying electric and magnetic dipole strengths (E1 and M1, respectively), particularly Pygmy Dipole Resonance (PDR) and Spin-flip M1 excitations, of atomic nuclei have drawn considerable attention in the last decade. The low-lying dipole strengths of {sup 50}Cr were studied with the method of nuclear resonance fluorescence up to 9.7 MeV, using bremsstrahlung provided by the superconducting Darmstadt electron linear accelerator S-DALINAC. Twenty-four spin-1 states were observed between 3.0 and 9.7 MeV excitation energy, 17 of those for the first time. The excited states' parities are determined through polarized photon scattering at the High Intensity gamma ray Source (HIγS), Triangle Universities Nuclear Laboratory (TUNL) in Durham, NC, USA. Microscopic calculations within the quasiparticle-phonon nuclear model are performed to interpret the dipole strength distribution of {sup 50}Cr. The experimental results of {sup 50}Cr are compared to data on its closed-shell N=28 isotone {sup 52}Cr and may provide information on the onset of the PDR in atomic nuclei.
Homomorphisms between JC*-algebras and Lie C*-algebras
Chun Gil PARK; Jin Chuan HOU; Sei Qwon OH
2005-01-01
It is shown that every almost *-homomorphism h: A → B of a unital JC*-algebra A to a unital JC*-algebra B is a *-homomorphism when h(rx) = rh(x) (r ＞ 1) for all x ∈ A, and that every almost linear mapping h: A → B is a *-homomorphism when h(2nu o y) = h(2nu) o h(y),h(3nu o y) = h(3nu) o h(y) or h(qnu o y) = h(qnu) o h(y) for all unitaries u ∈ A, all y ∈ A, and n = 0, 1, Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings.We prove that every almost *-homomorphism h: A → B of a unital Lie C*-algebra A to a unital Lie C*-algebra B is a *-homomorphism when h(rx) = rh(x) (r ＞ 1) for all x ∈ A.
Mutually Unbiased Bases and Orthogonal Decompositions of Lie Algebras
Boykin, P O; Tiep, P H; Wocjan, P; Sitharam, Meera; Tiep, Pham Huu; Wocjan, Pawel
2005-01-01
We establish a connection between the problem of constructing maximal collections of mutually unbiased bases (MUBs) and an open problem in the theory of Lie algebras. More precisely, we show that a collection of m MUBs in K^n gives rise to a collection of m Cartan subalgebras of the special linear Lie algebra sl_n(K) that are pairwise orthogonal with respect to the Killing form, where K=R or K=C. In particular, a complete collection of MUBs in C^n gives rise to a so-called orthogonal decomposition (OD) of sl_n(C). The converse holds if the Cartan subalgebras in the OD are also *-closed, i.e., closed under the adjoint operation. In this case, the Cartan subalgebras have unitary bases, and the above correspondence becomes equivalent to a result relating collections of MUBs to collections of maximal commuting classes of unitary error bases, i.e., orthogonal unitary matrices. It is a longstanding conjecture that ODs of sl_n(C) can only exist if n is a prime power. This corroborates further the general belief that...
The Watching-Eye Effect on Prosocial Lying
Ryo Oda
2015-07-01
Full Text Available Evidence shows that people tend to behave prosocially when they are in the presence of images depicting eyes. There are two proximate causes of the eyes effect. One involves positive motivation to gain future reward and the other involves negative motivation to avoid violating a norm. Although several studies have suggested that positive motivation is a strong candidate, these studies were unable to distinguish between adherence to norms and prosocial behavior. We investigated the watching-eyes effect in an experimental setting to determine whether the tendency of humans to violate norms voluntarily could be understood as prosocial behavior. We compared the tendency to tell “prosocial lies” in the presence of a depiction of stylized eyes (eyes condition with that involving no such depiction (control condition. Under the control condition, participants tended to tell lies that benefitted others, whereas the tendency toward prosocial lying disappeared under the eyes condition. This suggests that the desire to avoid violating norms by being honest is stronger than the desire to pursue a good reputation by demonstrating generosity when such violation might lead to serious costs.
Hybrid Topological Lie-Hamiltonian Learning in Evolving Energy Landscapes
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
In this Chapter, a novel bidirectional algorithm for hybrid (discrete + continuous-time) Lie-Hamiltonian evolution in adaptive energy landscape-manifold is designed and its topological representation is proposed. The algorithm is developed within a geometrically and topologically extended framework of Hopfield's neural nets and Haken's synergetics (it is currently designed in Mathematica, although with small changes it could be implemented in Symbolic C++ or any other computer algebra system). The adaptive energy manifold is determined by the Hamiltonian multivariate cost function H, based on the user-defined vehicle-fleet configuration matrix W, which represents the pseudo-Riemannian metric tensor of the energy manifold. Search for the global minimum of H is performed using random signal differential Hebbian adaptation. This stochastic gradient evolution is driven (or, pulled-down) by `gravitational forces' defined by the 2nd Lie derivatives of H. Topological changes of the fleet matrix W are observed during the evolution and its topological invariant is established. The evolution stops when the W-topology breaks down into several connectivity-components, followed by topology-breaking instability sequence (i.e., a series of phase transitions).
Radiative Decays of Low-Lying Excited-State Hyperons
Taylor, Simon [Rice Univ., Houston, TX (United States)
2000-05-01
The quark wave-functions of the lower-lying excited-state hyperons Lambda(1405), Sigma(1385), and Lambda(1520) are not well understood. For example, the Lambda(1405) may not be a regular three-quark state but a $\\bar{K}$N molecule. Several competing models have been proposed, but none have been convincingly eliminated. Measuring radiative decays provides a means of discriminating between the models. The radiative branching of ratios are predicted to be small (~1%), but the radiative widths vary by factors of 2-10 from model to model. The existing experimental data is sparse and inconsistent; moreover, the radiative decay of the Sigma(1385) has never been observed before (except for one event). These lower-lying excited state hypersons were produced in a tagged photon-beam experiment in the CLAS detector at TJNAF in the reaction gamma p → K^{+} Y* for photon energies from threshold to 2.4 GeV. The radiative branching ration for the Sigma^{0}(1385) relative to the Sigma^{0}(1385) → Lambda pi^{0} channel was measured to be 0.021 ± 0.008$+0.004\\atop{-0.007}$, corresponding to a partial width of 640 ± 270$+130\\atop{-220}$ keV.
Yin, Lijun; Weber, Bernd
2016-03-01
Can beneficial ends justify morally questionable means? To investigate how monetary outcomes influence the neural responses to lying, we used a modified, cheap talk sender-receiver game in which participants were the direct recipients of lies and truthful statements resulting in either beneficial or harmful monetary outcomes. Both truth-telling (vs lying) as well as beneficial (vs harmful) outcomes elicited higher activity in the nucleus accumbens. Lying (vs truth-telling) elicited higher activity in the supplementary motor area, right inferior frontal gyrus, superior temporal sulcus and left anterior insula. Moreover, the significant interaction effect was found in the left amygdala, which showed that the monetary outcomes modulated the neural activity in the left amygdala only when truth-telling rather than lying. Our study identified a neural network associated with the reception of lies and truth, including the regions linked to the reward process, recognition and emotional experiences of being treated (dis)honestly.
Random matrix theory, the exceptional Lie groups and L-functions
Keating, J P [School of Mathematics, University of Bristol, Bristol BS8 1TW, UK (United Kingdom); Linden, N [School of Mathematics, University of Bristol, Bristol BS8 1TW, UK (United Kingdom); Rudnick, Z [Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)
2003-03-28
There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices and value distributions within families of L-functions. These connections are extended here to non-classical groups. We focus on an explicit example: the exceptional Lie group G{sub 2}. The value distributions for characteristic polynomials associated with the 7- and 14-dimensional representations of G{sub 2}, defined with respect to the uniform invariant (Haar) measure, are calculated using two of the Macdonald constant term identities. A one-parameter family of L-functions over a finite field is described whose value distribution in the limit as the size of the finite field grows is related to that of the characteristic polynomials associated with the seven-dimensional representation of G{sub 2}. The random matrix calculations extend to all exceptional Lie groups.
Lie group invariant finite difference schemes for the neutron diffusion equation
Jaegers, P.J.
1994-06-01
Finite difference techniques are used to solve a variety of differential equations. For the neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference approximation of the diffusion equation, the invariance properties of the original differential equation have been incorporated into the finite difference equations. Using the concept of an invariant difference operator, the invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant difference equations were defined to lie upon a cell edged mesh as opposed to the standard difference equations, which lie upon a cell centered mesh. Results for a variety of source approximations showed that the invariant difference equations were able to determine the eigenvalue with greater accuracy, for a given mesh spacing, than the standard difference approximation. The local truncation errors for these invariant difference schemes were found to be highly dependent upon the source approximation used, and the type of source distribution played a greater role in determining the accuracy of the invariant difference scheme than the local truncation error.
Lying and Truth-Telling in Children: From Concept to Action
Xu, Fen; Bao, Xuehua; Fu, Genyue; Talwar, Victoria; Lee, Kang
2010-01-01
While there has been extensive research on children's moral knowledge about lying and truth-telling and their actual lie- or truth-telling behaviors, research to examine the relationship between the 2 is extremely rare. This study examined one hundred and twenty 7-, 9-, and 11-year-olds' moral understanding of lies and their actual lying behaviors in a politeness situation. Results revealed that as age increased, children increasingly evaluated others' lying in politeness situations less negatively and were more inclined to tell lies in such situations themselves. Contrary to previous findings, children's socio-moral knowledge about lying was significantly related to their actual behaviors particularly when children's rationales underlying their moral judgments were consistent with their motives for actual lie- or truth-telling in the politeness situation. PMID:20438462
The Killing form and maximal toral subalgebra of the complete Lie algebra
孟道骥; 王淑苹
1996-01-01
Although the Killing form of a complete Lie algebra is degenerate in general,its restrictions to maximal toral subalgebras are still nondegenerate.This fact presents a criterion to simple complete Lie algebras in terms of root system.
A Realization of Hom-Lie Algebras by Iso-Deformed Commutator Bracket
Xiuxian Li
2013-01-01
We construct classical Iso-Lie and Iso-Hom-Lie algebras in $gl(V)$ by twisted commutator bracket through Iso-deformation. We prove that they are simple. Their Iso-automorphisms and isotopies are also presented.
Deceptive Intentions: Can Cues to Deception Be Measured before a Lie Is Even Stated?
Ströfer, S; Noordzij, Matthijs L; Ufkes, E.G; Giebels, Ellen
2015-01-01
.... Both are related to increased sympathetic nervous system (SNS) activity. We hypothesized that SNS activity already rises during intentions to lie and, consequently, cues to deception can be detected before stating an actual lie...
Deceptive Intentions: Can Cues to Deception Be Measured before a Lie Is Even Stated?: e0125237
Sabine Ströfer; Matthijs L Noordzij; Elze G Ufkes; Ellen Giebels
2015-01-01
.... Both are related to increased sympathetic nervous system (SNS) activity. We hypothesized that SNS activity already rises during intentions to lie and, consequently, cues to deception can be detected before stating an actual lie...
Nonlinear wave evolution in VLASOV plasma: a lie-transform analysis
Cary, J.R.
1979-08-01
Nonlinear wave evolution in Vlasov plasma is analyzed using the Lie transform, a powerful mathematical tool which is applicable to Hamiltonian systems. The first part of this thesis is an exposition of the Lie transform. Dewar's general Lie transform theory is explained and is used to construct Deprit's Lie transform perturbation technique. The basic theory is illustrated by simple examples.
Zanette, Sarah; Gao, Xiaoqing; Brunet, Megan; Bartlett, Marian Stewart; Lee, Kang
2016-10-01
The current study used computer vision technology to examine the nonverbal facial expressions of children (6-11years old) telling antisocial and prosocial lies. Children in the antisocial lying group completed a temptation resistance paradigm where they were asked not to peek at a gift being wrapped for them. All children peeked at the gift and subsequently lied about their behavior. Children in the prosocial lying group were given an undesirable gift and asked if they liked it. All children lied about liking the gift. Nonverbal behavior was analyzed using the Computer Expression Recognition Toolbox (CERT), which employs the Facial Action Coding System (FACS), to automatically code children's facial expressions while lying. Using CERT, children's facial expressions during antisocial and prosocial lying were accurately and reliably differentiated significantly above chance-level accuracy. The basic expressions of emotion that distinguished antisocial lies from prosocial lies were joy and contempt. Children expressed joy more in prosocial lying than in antisocial lying. Girls showed more joy and less contempt compared with boys when they told prosocial lies. Boys showed more contempt when they told prosocial lies than when they told antisocial lies. The key action units (AUs) that differentiate children's antisocial and prosocial lies are blink/eye closure, lip pucker, and lip raise on the right side. Together, these findings indicate that children's facial expressions differ while telling antisocial versus prosocial lies. The reliability of CERT in detecting such differences in facial expression suggests the viability of using computer vision technology in deception research. Copyright © 2016 Elsevier Inc. All rights reserved.
Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System
FANG Jian-Hui
2003-01-01
The Mei symmetry and the Lie symmetry of a rotational relativistic variable masssystem are studied. Thedefinitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system aregiven. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Meisymmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.
Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System
FANGJian-Hui
2003-01-01
The Mei symmetry and the Lie symmetry of a rotational relativistic variable mass system are studied. The definitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system are given. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.
New Applications of a Kind of Infinitesimal-Operator Lie Algebra
Honwah Tam
2016-01-01
Full Text Available Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. A corresponding discrete equation approximating it is given as well. Finally, we make use of the Lie algebras to generate some new integrable systems including (1+1 and (2+1 dimensions.
An introduction to some novel applications of Lie algebra cohomology and physics
de Azcárraga, J A; Bueno, J C P
1998-01-01
After a self-contained introduction to Lie algebra cohomology, we present some recent applications in mathematics and in physics. Contents: 1. Preliminaries: L_X, i_X, d 2. Elementary differential geometry on Lie groups 3. Lie algebra cohomology: a brief introduction 4. Symmetric polynomials and higher order cocycles 5. Higher order simple and SH Lie algebras 6. Higher order generalized Poisson structures 7. Relative cohomology, coset spaces and effective WZW actions
Non-solvable contractions of semisimple Lie algebras in low dimension
Campoamor-Stursberg, R [Dpto. GeometrIa y TopologIa, Fac. CC. Matematicas, Universidad Complutense de Madrid, Plaza de Ciencias, 3, E-28040 Madrid (Spain)
2007-05-18
The problem of non-solvable contractions of Lie algebras is analysed. By means of a stability theorem, the problem is shown to be deeply related to the embeddings among semisimple Lie algebras and the resulting branching rules for representations. With this procedure, we determine all deformations of indecomposable Lie algebras having a nontrivial Levi decomposition onto semisimple Lie algebras of dimension n {<=} 8, and obtain the non-solvable contractions of the latter class of algebras.
La propri\\'et\\'e de Dixmier pour les alg\\`ebres de Lie de champs de vecteurs
Raïs, Mustapha
2009-01-01
Given a linear representation $\\rho : \\mathfrak{g} \\longrightarrow \\mathfrak{g}\\ell(V)$ of a Lie algebra $\\mathfrak{g}$, one can define a linear representation $\\rho_m : \\mathfrak{g}_m \\longrightarrow \\mathfrak{g}\\ell(V^m)$ of the generalized Takiff algebra $\\mathfrak{g}_m$. It is proved here that the vector fields defined by $\\rho_m$ on $V^m$ do have the Dixmier property if those defined by $\\rho$ have the same property. Examples where the result applies are given and in particular, those of the adjoint or coadjoint representations of Takiff algebras.
Lie Group Classifications and Non-differentiable Solutions for Time-Fractional Burgers Equation
WU Guo-Cheng
2011-01-01
Lie group method provides an efficient tool to solve nonlinear partial differential equations.This paper suggests Lie group method for fractional partial differential equations.A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.
Homogeneous Construction of the Toroidal Lie Algebra of Type A1
Haifeng Lian; Cui Chen; Qinzhu Wen
2007-01-01
In this paper,we consider an analogue of the level two homogeneous construc-tion of the affine Kac-Moody algebra A1(1) by vertex operators.We construct modules for the toroidal Lie algebra and the extended toroidal Lie algebra of type A1.We also prove that the module is completely reducible for the extended toroidal Lie algebra.
A natural differential calculus on Lie bialgebras with dual of triangular type
Hijligenberg, N.W. van den; Martini, R.
1995-01-01
We prove that for a specific class of Lie bialgebras, there exists a natural differential calculus. This class consists of the Lie bialgebras for which the dual Lie bialgebra is of triangular type. The differential calculus is explicitly constructed with the help of the $R$-matrix from the dual. The