Automorphisms of p-compact groups and their root data

DEFF Research Database (Denmark)

Andersen, Kasper K. S.; Grodal, Jesper Kragh

2008-01-01

We construct a model for the space of automorphisms of a connected p–compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer automorphism group of a p–compact group can be lifted to a group...... action, analogous to   a classical theorem of de Siebenthal for compact Lie groups. The model of this paper is used in a crucial way in our paper `The classification of 2-compact groups' [arXiv:math.AT/0611437], where we prove the conjectured classification of 2–compact groups and determine...... their automorphism spaces....

The formalism of Lie groups

Energy Technology Data Exchange (ETDEWEB)

Salam, A. [Imperial College of Science and Technology, London (United Kingdom)

1963-01-15

Throughout the history of quantum theory, a battle has raged between the amateurs and professional group theorists. The amateurs have maintained that everything one needs in the theory of groups can be discovered by the light of nature provided one knows how to multiply two matrices. In support of this claim, they of course, justifiably, point to the successes of that prince of amateurs in this field, Dirac, particularly with the spinor representations of the Lorentz group. As an amateur myself, I strongly believe in the truth of the non-professionalist creed. I think perhaps there is not much one has to learn in the way of methodology from the group theorists except caution. But this does not mean one should not be aware of the riches which have been amassed over the course of years particularly in that most highly developed of all mathematical disciplines - the theory of Lie groups. My lectures then are an amateur's attempt to gather some of the fascinating results for compact simple Lie groups which are likely to be of physical interest. I shall state theorems; and with a physicist's typical unconcern rarely, if ever, shall I prove these. Throughout, the emphasis will be to show the close similarity of these general groups with that most familiar of all groups, the group of rotations in three dimensions.

Analytic parameter dependence of Harish-Chandra modules for real reductive Lie groups - a family affair

NARCIS (Netherlands)

van der Noort, V.

2009-01-01

This thesis is written in the subfield of mathematics known as representation theory of real reductive Lie groups. Let G be a Lie group in the Harish-Chandra class with maximal compact subgroup K and Lie algebra g. Let Omega be a connected complex manifold. By a family of G-representations

Quasi-Lie algebras and Lie groups

International Nuclear Information System (INIS)

Momo Bangoura

2006-07-01

In this work, we define the quasi-Poisson Lie quasigroups, dual objects to the quasi-Poisson Lie groups and we establish the correspondence between the local quasi-Poisson Lie quasigoups and quasi-Lie bialgebras (up to isomorphism). (author) [fr

Target-space duality between simple compact Lie groups and Lie algebras under the Hamiltonian formalism. Pt. 1. Remnants of duality at the classic level

International Nuclear Information System (INIS)

Alvarez, O.; Liu Chienhao

1996-01-01

It has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie group G with a bi-invariant metric and a generating function Γ suggested in the physics literature, we follow the above line of thought and work out the canonical transformation Φ generated by Γ together with an Ad-invariant metric and a B-field on the associated Lie algebra g of G so that G and g form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation Φ including a careful analysis of its domain and image. The geometry of the T-dual structure on g is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper. (orig.). With 4 figs

Lie groups and Lie algebras for physicists

CERN Document Server

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.

Lie groups, lie algebras, and representations an elementary introduction

CERN Document Server

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...

Basic gerbe over non simply connected compact groups

OpenAIRE

Gawedzki, Krzysztof; Reis, Nuno

2003-01-01

We present an explicit construction of the basic bundle gerbes with connection over all connected compact simple Lie groups. These are geometric objects that appear naturally in the Lagrangian approach to the WZW conformal field theories. Our work extends the recent construction of E. Meinrenken \\cite{Meinr} restricted to the case of simply connected groups.

Simple Lie groups without the approximation property

DEFF Research Database (Denmark)

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...... on the space M0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely, SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center...

Property A and Coarse Embedding for Locally Compact Groups

DEFF Research Database (Denmark)

Li, Kang

property A. In a joint work with Knudby, we characterize the connected simple Lie groups with the discrete topology that have different approximation properties (see Article B). Moreover, we give a contractive Schur multiplier characterization of locally compact groups coarsely embeddable into Hilbert......In the study of the Novikov conjecture, property A and coarse embedding of metric spaces were introduced by Yu and Gromov, respectively. The main topic of the thesis is property A and coarse embedding for locally compact second countable groups. We prove that many of the results that are known...... to hold in the discrete setting, hold also in the locally compact setting.In a joint work with Deprez, we show that property A is equivalent to amenability at infinity and the strong Novikov conjecture is true for every locally compact group that embeds coarsely into a Hilbert space (see Article A...

Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations

Energy Technology Data Exchange (ETDEWEB)

Larouche, M [Departement de Mathematiques et Statistique, Universite de Montreal, 2920 chemin de la Tour, Montreal, Quebec H3T 1J4 (Canada); Lemire, F W [Department of Mathematics, University of Windsor, Windsor, Ontario (Canada); Patera, J, E-mail: larouche@dms.umontreal.ca, E-mail: lemire@uwindsor.ca, E-mail: patera@crm.umontreal.ca [Centre de Recherches Mathematiques, Universite de Montreal, CP 6128-Centre ville, Montreal, Quebec H3C 3J7 (Canada)

2011-10-14

In this paper, we present a new, uniform and comprehensive description of centralizers of the maximal regular subgroups in compact simple Lie groups of all types and ranks. The centralizer is either a direct product of finite cyclic groups, a continuous group of rank 1, or a product, not necessarily direct, of a continuous group of rank 1 with a finite cyclic group. Explicit formulas for the action of such centralizers on irreducible representations of the simple Lie algebras are given. (paper)

Theory of super LIE groups

International Nuclear Information System (INIS)

Prakash, M.

1985-01-01

The theory of supergravity has attracted increasing attention in the recent years as a unified theory of elementary particle interactions. The superspace formulation of the theory is highly suggestive of an underlying geometrical structure of superspace. It also incorporates the beautifully geometrical general theory of relativity. It leads us to believe that a better understanding of its geometry would result in a better understanding of the theory itself, and furthermore, that the geometry of superspace would also have physical consequences. As a first step towards that goal, we develop here a theory of super Lie groups. These are groups that have the same relation to a super Lie algebra as Lie groups have to a Lie algebra. More precisely, a super Lie group is a super-manifold and a group such that the group operations are super-analytic. The super Lie algebra of a super Lie group is related to the local properties of the group near the identity. This work develops the algebraic and super-analytical tools necessary for our theory, including proofs of a set of existence and uniqueness theorems for a class of super-differential equations

Real representations of Lie groups and a theorem of H. Pittie

International Nuclear Information System (INIS)

Freitas, R.

1992-01-01

In this paper, we prove a structure theorem of the real representation ring RO(T) as a module over the real representation ring RO(G), where G is a compact, connected and simply connected Lie group and T is a maximal torus of G. This provides a real version to a theorem of H. Pittie. (author). 24 refs

The structure of complex Lie groups

CERN Document Server

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 ...

Statistics on Lie groups: A need to go beyond the pseudo-Riemannian framework

Science.gov (United States)

Miolane, Nina; Pennec, Xavier

2015-01-01

Lie groups appear in many fields from Medical Imaging to Robotics. In Medical Imaging and particularly in Computational Anatomy, an organ's shape is often modeled as the deformation of a reference shape, in other words: as an element of a Lie group. In this framework, if one wants to model the variability of the human anatomy, e.g. in order to help diagnosis of diseases, one needs to perform statistics on Lie groups. A Lie group G is a manifold that carries an additional group structure. Statistics on Riemannian manifolds have been well studied with the pioneer work of Fréchet, Karcher and Kendall [1, 2, 3, 4] followed by others [5, 6, 7, 8, 9]. In order to use such a Riemannian structure for statistics on Lie groups, one needs to define a Riemannian metric that is compatible with the group structure, i.e a bi-invariant metric. However, it is well known that general Lie groups which cannot be decomposed into the direct product of compact and abelian groups do not admit a bi-invariant metric. One may wonder if removing the positivity of the metric, thus asking only for a bi-invariant pseudo-Riemannian metric, would be sufficient for most of the groups used in Computational Anatomy. In this paper, we provide an algorithmic procedure that constructs bi-invariant pseudo-metrics on a given Lie group G. The procedure relies on a classification theorem of Medina and Revoy. However in doing so, we prove that most Lie groups do not admit any bi-invariant (pseudo-) metric. We conclude that the (pseudo-) Riemannian setting is not the richest setting if one wants to perform statistics on Lie groups. One may have to rely on another framework, such as affine connection space.

The BRST complex and the cohomology of compact lie algebras

International Nuclear Information System (INIS)

Holten, J.W. van

1990-02-01

The authors construct the BRST and anti-BRST operator for a compact Lie algebra which is a direct sum of abelian and simple ideals. Two different inner products are defined on the ghost space and the hermiticity propeties of the ghost and BRST operators with respect to these inner products are discussed. A decomposition theorem for ghost states is derived and the cohomology of the BRST complex is shown to reduce to the standard Lie-algebra cohomology. The authors show that the cohomology classes of the Lie algebra are given by all invariant anti-symmetric tensors and explain how thse can be obtained as zero-modes of an invariant operator in the representation space of the ghosts. Explicit examples are given. (author) 24 refs

A comparison between star products on regular orbits of compact Lie groups

International Nuclear Information System (INIS)

Fioresi, R.; Lledo, M.A.

2002-01-01

In this paper, an algebraic and a differential star product defined on a regular coadjoint orbit of a compact semisimple group are compared. It has been proved that there is an injective algebra homomorphism between the algebra of polynomials with the algebraic star product and the algebra of differential functions with the differential star product structure. (author)

Lie groups, Lie algebras, and some of their applications

CERN Document Server

Gilmore, Robert

1974-01-01

Lie group theory plays an increasingly important role in modern physical theories. Many of its calculations remain fundamentally unchanged from one field of physics to another, altering only in terms of symbols and the language. Using the theory of Lie groups as a unifying vehicle, concepts and results from several fields of physics can be expressed in an extremely economical way. With rigor and clarity, this text introduces upper-level undergraduate students to Lie group theory and its physical applications.An opening discussion of introductory concepts leads to explorations of the classical

Harmonic analysis and global solvability of a differential operator invariant on motion groups and semi-simple Lie groups

International Nuclear Information System (INIS)

El-Hussein, K.

1991-08-01

Let V be a real finite dimensional vector space and let K be a connected compact Lie group, which acts on V by means of a continuous linear representation ρ. Let G=V x p K be the motion group which is the semi-direct product of V by K and let P be an invariant differential operator on G. In this paper we give a necessary and sufficient condition for the global solvability of P on G. Now let G be a connected semi-simple Lie group with finite centre and let P be an invariant differential operator on G. We give also a necessary and sufficient condition for the global solvability of P on G. (author). 8 refs

Lie groups and algebraic groups

Indian Academy of Sciences (India)

We give an exposition of certain topics in Lie groups and algebraic groups. This is not a complete ... of a polynomial equation is equivalent to the solva- bility of the equation ..... to a subgroup of the group of roots of unity in k (in particular, it is a ...

The structure of compact groups a primer for the student, a handbook for the expert

CERN Document Server

Hofmann, Karl H

2013-01-01

Dealing with subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book - now in its third revised and augmented edition - has been conceived with the dual purpose of providing a text book for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups. After a gentle introduction to compact groups and their representation theory, the book presents self-contained courses on linear Lie groups,

The Ultraviolet and Infrared Star Formation Rates of Compact Group Galaxies: An Expanded Sample

Science.gov (United States)

Lenkic, Laura; Tzanavaris, Panayiotis; Gallagher, Sarah C.; Desjardins, Tyler D.; Walker, Lisa May; Johnson, Kelsey E.; Fedotov, Konstantin; Charlton, Jane; Cardiff, Ann H.; Durell, Pat R.

2016-01-01

Compact groups of galaxies provide insight into the role of low-mass, dense environments in galaxy evolution because the low velocity dispersions and close proximity of galaxy members result in frequent interactions that take place over extended time-scales. We expand the census of star formation in compact group galaxies by Tzanavaris et al. (2010) and collaborators with Swift UVOT, Spitzer IRAC and MIPS 24 m photometry of a sample of 183 galaxies in 46 compact groups. After correcting luminosities for the contribution from old stellar populations, we estimate the dust-unobscured star formation rate (SFRUV) using the UVOT uvw2 photometry. Similarly, we use the MIPS 24 m photometry to estimate the component of the SFR that is obscured by dust (SFRIR). We find that galaxies which are MIR-active (MIR-red), also have bluer UV colours, higher specific SFRs, and tend to lie in Hi-rich groups, while galaxies that are MIR-inactive (MIR-blue) have redder UV colours, lower specific SFRs, and tend to lie in Hi-poor groups. We find the SFRs to be continuously distributed with a peak at about 1 M yr1, indicating this might be the most common value in compact groups. In contrast, the specific SFR distribution is bimodal, and there is a clear distinction between star-forming and quiescent galaxies. Overall, our results suggest that the specific SFR is the best tracer of gas depletion and galaxy evolution in compact groups.

Non-commutative representation for quantum systems on Lie groups

Energy Technology Data Exchange (ETDEWEB)

Raasakka, Matti Tapio

2014-01-27

space path integral with the help of the non-commutative dual variables. In studying the classical limit of the path integral, we show that we recover the correct classical equations of motion for the particle, if we account for the deformation of the phase space in the variational calculus. The non-commutative variables correspond in this limit to the classical momentum variables, further verifying their physical interpretation. We conclude that the non-commutative harmonic analysis facilitates a convenient study of the classical limit of quantum dynamics on a Lie group even if the group is compact, in which case variational calculus cannot easily be applied. As the second physics application, we repeat our above considerations for the case of Ponzano-Regge spin foam model for 3-dimensional quantum gravity. The non-commutative dual variables correspond in this case to discrete metric variables, thus illuminating the geometrical interpretation of the model. Again, we find that a convenient study of the classical limit is made possible through the non-commutative phase space path integral.

Non-commutative representation for quantum systems on Lie groups

International Nuclear Information System (INIS)

Raasakka, Matti Tapio

2014-01-01

integral with the help of the non-commutative dual variables. In studying the classical limit of the path integral, we show that we recover the correct classical equations of motion for the particle, if we account for the deformation of the phase space in the variational calculus. The non-commutative variables correspond in this limit to the classical momentum variables, further verifying their physical interpretation. We conclude that the non-commutative harmonic analysis facilitates a convenient study of the classical limit of quantum dynamics on a Lie group even if the group is compact, in which case variational calculus cannot easily be applied. As the second physics application, we repeat our above considerations for the case of Ponzano-Regge spin foam model for 3-dimensional quantum gravity. The non-commutative dual variables correspond in this case to discrete metric variables, thus illuminating the geometrical interpretation of the model. Again, we find that a convenient study of the classical limit is made possible through the non-commutative phase space path integral.

A decomposition theorem for compact groups with an application to supercompactness

Czech Academy of Sciences Publication Activity Database

Kubiś, Wieslaw; Turek, S.

2011-01-01

Roč. 9, č. 3 (2011), s. 593-602 ISSN 1895-1074 R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Simple compact Lie group * Supercompact space Subject RIV: BA - General Mathematics Impact factor: 0.440, year: 2011 http://www.springerlink.com/content/h86v44387542637r/

Algebras of functions on compact quantum groups, Schubert cells and quantum tori

International Nuclear Information System (INIS)

Levendorskij, S.; Soibelman, Ya.

1991-01-01

The structure of Poisson Lie groups on a simple compact group are parametrized by pairs (a, u), where aelement ofR, uelement ofΛ 2 f R , and f R is a real Cartan subalgebra of complexification of Lie algebra of the group in question. In the present article the description of the symplectic leaves for all pairs (a, u) is given. Also, the corresponding quantized algebras of functions are constructed and their irreducible representations are described. In the course of investigation Schubert cells and quantum tori appear. At the end of the article the quantum analog of the Weyl group is constructed and some of its applications, among them the formula for the universal R-matrix, are given. (orig.)

Elementary construction of graded lie groups

International Nuclear Information System (INIS)

Scheunert, M.; Rittenberg, V.

1977-06-01

We show how the definitions of the classical Lie groups have to be modified in the case where Grassmann variables are present. In particular, we construct the general linear, the special linear and the orthosymplectic graded Lie groups. Special attention is paid to the question of how to formulate an adequate 'unitarity condition'. (orig.) [de

Essays in the history of Lie groups and algebraic groups

CERN Document Server

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...

Introduction to the theory of Lie groups

CERN Document Server

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.

S7 without any construction of Lie group

International Nuclear Information System (INIS)

Zhou Jian; Xu Senlin.

1988-12-01

It was proved that the sphere S n is a parallelizable manifold if and only if n = 1,3 or 7, and that S n is an H-space if and only if n = 0,1,3 or 7. Because a Lie group must necessarily be a parallelizable manifold and also an H-space, naturally one asks that S n is a Lie group for n = 0, 1,3 or 7? In this paper we prove that S 7 is not a Lie group, and it is not even a topological group. Therefore, S n is a Lie group (or a topological group) if and only if n = 0,1,3. (author). 11 refs

Enveloping algebras of Lie groups with descrete series

International Nuclear Information System (INIS)

Nguyen huu Anh; Vuong manh Son

1990-09-01

In this article we shall prove that the enveloping algebra of the Lie algebra of some unimodular Lie group having discrete series, when localized at some element of the center, is isomorphic to the tensor product of a Weyl algebra over the ring of Laurent polynomials of one variable and the enveloping algebra of some reductive Lie algebra. In particular, it will be proved that the Lie algebra of a unimodular solvable Lie group having discrete series satisfies the Gelfand-Kirillov conjecture. (author). 6 refs

Physically detached 'compact groups'

Science.gov (United States)

Hernquist, Lars; Katz, Neal; Weinberg, David H.

1995-01-01

A small fraction of galaxies appear to reside in dense compact groups, whose inferred crossing times are much shorter than a Hubble time. These short crossing times have led to considerable disagreement among researchers attempting to deduce the dynamical state of these systems. In this paper, we suggest that many of the observed groups are not physically bound but are chance projections of galaxies well separated along the line of sight. Unlike earlier similar proposals, ours does not require that the galaxies in the compact group be members of a more diffuse, but physically bound entity. The probability of physically separated galaxies projecting into an apparent compact group is nonnegligible if most galaxies are distributed in thin filaments. We illustrate this general point with a specific example: a simulation of a cold dark matter universe, in which hydrodynamic effects are included to identify galaxies. The simulated galaxy distribution is filamentary and end-on views of these filaments produce apparent galaxy associations that have sizes and velocity dispersions similar to those of observed compact groups. The frequency of such projections is sufficient, in principle, to explain the observed space density of groups in the Hickson catalog. We discuss the implications of our proposal for the formation and evolution of groups and elliptical galaxies. The proposal can be tested by using redshift-independent distance estimators to measure the line-of-sight spatial extent of nearby compact groups.

Reflection Positive Stochastic Processes Indexed by Lie Groups

Science.gov (United States)

Jorgensen, Palle E. T.; Neeb, Karl-Hermann; Ólafsson, Gestur

2016-06-01

Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in representation theory, it is related to the Cartan duality of symmetric Lie groups (Lie groups with an involution) and results in a transformation of a unitary representation of a symmetric Lie group to a unitary representation of its Cartan dual. In this article we continue our investigation of representation theoretic aspects of reflection positivity by discussing reflection positive Markov processes indexed by Lie groups, measures on path spaces, and invariant gaussian measures in spaces of distribution vectors. This provides new constructions of reflection positive unitary representations.

Topological and homological properties of the orbit space of a compact linear Lie group with commutative connected component

OpenAIRE

Styrt, O. G.

2016-01-01

The problem in question is whether the quotient space of a compact linear group is a topological manifold and whether it is a homological manifold. In the paper, the case of an infinite group with commutative connected component is considered.

Lie groups for pedestrians

CERN Document Server

Lipkin, Harry J

2002-01-01

According to the author of this concise, high-level study, physicists often shy away from group theory, perhaps because they are unsure which parts of the subject belong to the physicist and which belong to the mathematician. However, it is possible for physicists to understand and use many techniques which have a group theoretical basis without necessarily understanding all of group theory. This book is designed to familiarize physicists with those techniques. Specifically, the author aims to show how the well-known methods of angular momentum algebra can be extended to treat other Lie group

Deriving the largest expected number of elementary particles in the standard model from the maximal compact subgroup H of the exceptional Lie group E7(-5)

International Nuclear Information System (INIS)

El Naschie, M.S.

2008-01-01

The maximal number of elementary particles which could be expected to be found within a modestly extended energy scale of the standard model was found using various methods to be N = 69. In particular using E-infinity theory the present Author found the exact transfinite expectation value to be =α-bar o /2≅69 where α-bar o =137.082039325 is the exact inverse fine structure constant. In the present work we show among other things how to derive the exact integer value 69 from the exceptional Lie symmetry groups hierarchy. It is found that the relevant number is given by dim H = 69 where H is the maximal compact subspace of E 7(-5) so that N = dim H = 69 while dim E 7 = 133

Lie groups and grand unified theories

International Nuclear Information System (INIS)

Gubitoso, M.D.

1987-01-01

This work presents some concepts in group theory and Lie algebras and, at same time, shows a method to study and work with semisimple Lie groups, based on Dynkin diagrams. The aproach taken is not completely formal, but it presents the main points of the elaboration of the method, so its mathematical basis is designed with the purpose of making the reading not so cumbersome to those who are interested only in a general picture of the method and its usefulness. At the end it is shown a brief review of gauge theories and two grand-unification models based on SO(13) and E 7 gauge groups. (author) [pt

Uncertainty Principles on Two Step Nilpotent Lie Groups

Indian Academy of Sciences (India)

Abstract. 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.

Anti-Kählerian Geometry on Lie Groups

Science.gov (United States)

Fernández-Culma, Edison Alberto; Godoy, Yamile

2018-03-01

Let G be a Lie group of even dimension and let ( g, J) be a left invariant anti-Kähler structure on G. In this article we study anti-Kähler structures considering the distinguished cases where the complex structure J is abelian or bi-invariant. We find that if G admits a left invariant anti-Kähler structure ( g, J) where J is abelian then the Lie algebra of G is unimodular and ( G, g) is a flat pseudo-Riemannian manifold. For the second case, we see that for any left invariant metric g for which J is an anti-isometry we obtain that the triple ( G, g, J) is an anti-Kähler manifold. Besides, given a left invariant anti-Hermitian structure on G we associate a covariant 3-tensor 𝜃 on its Lie algebra and prove that such structure is anti-Kähler if and only if 𝜃 is a skew-symmetric and pure tensor. From this tensor we classify the real 4-dimensional Lie algebras for which the corresponding Lie group has a left invariant anti-Kähler structure and study the moduli spaces of such structures (up to group isomorphisms that preserve the anti-Kähler structures).

Lie Algebras Associated with Group U(n)

International Nuclear Information System (INIS)

Zhang Yufeng; Dong Huanghe; Honwah Tam

2007-01-01

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

Non-coboundary Poisson–Lie structures on the book group

International Nuclear Information System (INIS)

Ballesteros, Ángel; Blasco, Alfonso; Musso, Fabio

2012-01-01

All possible Poisson–Lie (PL) structures on the 3D real Lie group generated by a dilation and two commuting translations are obtained. Their classification is fully performed by relating these PL groups to the corresponding Lie bialgebra structures on the corresponding ‘book’ Lie algebra. By construction, all these Poisson structures are quadratic Poisson–Hopf algebras for which the group multiplication is a Poisson map. In contrast to the case of simple Lie groups, it turns out that most of the PL structures on the book group are non-coboundary ones. Moreover, from the viewpoint of Poisson dynamics, the most interesting PL book structures are just some of these non-coboundaries, which are explicitly analysed. In particular, we show that the two different q-deformed Poisson versions of the sl(2, R) algebra appear as two distinguished cases in this classification, as well as the quadratic Poisson structure that underlies the integrability of a large class of 3D Lotka–Volterra equations. Finally, the quantization problem for these PL groups is sketched. (paper)

Quantum algebras as quantizations of dual Poisson–Lie groups

International Nuclear Information System (INIS)

Ballesteros, Ángel; Musso, Fabio

2013-01-01

A systematic computational approach for the explicit construction of any quantum Hopf algebra (U z (g), Δ z ) starting from the Lie bialgebra (g, δ) that gives the first-order deformation of the coproduct map Δ z is presented. The procedure is based on the well-known ‘quantum duality principle’, namely the fact that any quantum algebra can be viewed as the quantization of the unique Poisson–Lie structure (G*, Λ g ) on the dual group G*, which is obtained by exponentiating the Lie algebra g* defined by the dual map δ*. From this perspective, the coproduct for U z (g) is just the pull-back of the group law for G*, and the Poisson analogues of the quantum commutation rules for U z (g) are given by the unique Poisson–Lie structure Λ g on G* whose linearization is the Poisson analogue of the initial Lie algebra g. This approach is shown to be a very useful technical tool in order to solve the Lie bialgebra quantization problem explicitly since, once a Lie bialgebra (g, δ) is given, the full dual Poisson–Lie group (G*, Λ) can be obtained either by applying standard Poisson–Lie group techniques or by implementing the algorithm presented here with the aid of symbolic manipulation programs. As a consequence, the quantization of (G*, Λ) will give rise to the full U z (g) quantum algebra, provided that ordering problems are appropriately fixed through the choice of certain local coordinates on G* whose coproduct fulfils a precise ‘quantum symmetry’ property. The applicability of this approach is explicitly demonstrated by reviewing the construction of several instances of quantum deformations of physically relevant Lie algebras such as sl(2,R), the (2+1) anti-de Sitter algebra so(2, 2) and the Poincaré algebra in (3+1) dimensions. (paper)

On approximation of Lie groups by discrete subgroups

Indian Academy of Sciences (India)

2016-08-26

Aug 26, 2016 ... 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 ...

Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces

Directory of Open Access Journals (Sweden)

Przemysław Górka

2014-01-01

Full Text Available We continue our research on Sobolev spaces on locally compact abelian (LCA groups motivated by our work on equations with infinitely many derivatives of interest for string theory and cosmology. In this paper, we focus on compact embedding results and we prove an analog for LCA groups of the classical Rellich lemma and of the Rellich-Kondrachov compactness theorem. Furthermore, we introduce Sobolev spaces on subsets of LCA groups and study its main properties, including the existence of compact embeddings into Lp-spaces.

An introduction to Lie group integrators – basics, new developments and applications

International Nuclear Information System (INIS)

Celledoni, Elena; Marthinsen, Håkon; Owren, Brynjulf

2014-01-01

We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion of discrete gradient methods is generalised to Lie groups

Lie symmetries and differential galois groups of linear equations

NARCIS (Netherlands)

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

Invariant differential operators for non-compact Lie groups: the SO* (12) case

Science.gov (United States)

Dobrev, V. K.

2015-04-01

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra so* (12). We give the main multiplets of indecomposable elementary representations. Due to the recently established parabolic relations the multiplet classification results are valid also for the algebra so(6, 6) with suitably chosen maximal parabolic subalgebra.

Where are compact groups in the local Universe?

Science.gov (United States)

Díaz-Giménez, Eugenia; Zandivarez, Ariel

2015-06-01

Aims: The purpose of this work is to perform a statistical analysis of the location of compact groups in the Universe from observational and semi-analytical points of view. Methods: We used the velocity-filtered compact group sample extracted from the Two Micron All Sky Survey for our analysis. We also used a new sample of galaxy groups identified in the 2M++ galaxy redshift catalogue as tracers of the large-scale structure. We defined a procedure to search in redshift space for compact groups that can be considered embedded in other overdense systems and applied this criterion to several possible combinations of different compact and galaxy group subsamples. We also performed similar analyses for simulated compact and galaxy groups identified in a 2M++ mock galaxy catalogue constructed from the Millennium Run Simulation I plus a semi-analytical model of galaxy formation. Results: We observed that only ~27% of the compact groups can be considered to be embedded in larger overdense systems, that is, most of the compact groups are more likely to be isolated systems. The embedded compact groups show statistically smaller sizes and brighter surface brightnesses than non-embedded systems. No evidence was found that embedded compact groups are more likely to inhabit galaxy groups with a given virial mass or with a particular dynamical state. We found very similar results when the analysis was performed using mock compact and galaxy groups. Based on the semi-analytical studies, we predict that 70% of the embedded compact groups probably are 3D physically dense systems. Finally, real space information allowed us to reveal the bimodal behaviour of the distribution of 3D minimum distances between compact and galaxy groups. Conclusions: The location of compact groups should be carefully taken into account when comparing properties of galaxies in environments that are a priori different. Appendices are available in electronic form at http://www.aanda.orgFull Tables B.1 and B.2

Controllability of linear vector fields on Lie groups

International Nuclear Information System (INIS)

Ayala, V.; Tirao, J.

1994-11-01

In this paper, we shall deal with a linear control system Σ defined on a Lie group G with Lie algebra g. The dynamic of Σ is determined by the drift vector field which is an element in the normalizer of g in the Lie algebra of all smooth vector field on G and by the control vectors which are elements in g considered as left-invariant vector fields. We characterize the normalizer of g identifying vector fields on G with C ∞ -functions defined on G into g. For this class of control systems we study algebraic conditions for the controllability problem. Indeed, we prove that if the drift vector field has a singularity then the Lie algebra rank condition is necessary for the controllability property, but in general this condition does not determine this property. On the other hand, we show that the rank (ad-rank) condition is sufficient for the controllability of Σ. In particular, we extend the fundamental Kalman's theorem when G is an Abelian connected Lie group. Our work is related with a paper of L. Markus and we also improve his results. (author). 7 refs

Invariant subsets under compact quantum group actions

OpenAIRE

Huang, Huichi

2012-01-01

We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable spaces with infinitely many points are not quantum homogeneous spaces.

Transformation groups and Lie algebras

CERN Document Server

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.

Explaining compact groups as change alignments

International Nuclear Information System (INIS)

Mamon, G.A.

1990-01-01

The physical nature of the apparently densest groups of galaxies, known as compact groups is a topic of some recent controversy, despite the detailed observations of a well-defined catalog of 100 isolated compact groups compiled by Hickson (1982). Whereas many authors have espoused the view that compact groups are bound systems, typically as dense as they appear in projection on the sky (e.g., Williams ampersand Rood 1987; Sulentic 1987; Hickson ampersand Rood 1988), others see them as the result of chance configurations within larger systems, either in 1D (chance alignments: Mamon 1986; Walke ampersand Mamon 1989), or in 3D (transient cores: Rose 1979). As outlined in the companion review to this contribution (Mamon, in these proceedings), the implication of Hickson's compact groups (HCGs) being dense bound systems is that they would then constitute the densest isolated systems of galaxies in the Universe and the privileged site for galaxy interactions. In a previous paper (Mamon 1986), the author reviewed the arguments given for the different theories of compact groups. Since then, a dozen papers have been published on the subject, including a thorough and perceptive review by White (1990), thus more than doubling the amount written on the subject. Here, the author first enumerates the arguments that he brought up in 1986 substantiating the chance alignment hypothesis, then he reviews the current status of the numerous recent arguments arguing against chance alignments and/or for the bound dense group hypothesis (both for the majority of HCGs but not all of them), and finally he reconsiders each one of these anti-chance alignment arguments and shows that, rather than being discredited, the chance alignment hypothesis remains a fully consistent explanation for the nature of compact groups

Observational properties of compact groups of galaxies

International Nuclear Information System (INIS)

Hickson, P.

1990-01-01

Compact groups are small, relatively isolated, systems of galaxies with projected separations comparable to the diameters of the galaxies themselves. Two well-known examples are Stephan's Quintet (Stephan, 1877) and Seyfert's Sextet (Seyfert 1948a,b). In groups such as these, the apparent space density of galaxies approaches 10(exp 6) Mpc(sub -3), denser even than the cores of rich clusters. The apparent unlikeliness of the chance occurrence of such tight groupings lead Ambartsumyan (1958, 1975) to conclude that compact groups must be physically dense systems. This view is supported by clear signs of galaxy interactions that are seen in many groups. Spectroscopic observations reveal that typical relative velocities of galaxies in the groups are comparable to their internal stellar velocities. This should be conducive to strong gravitational interactions - more so than in rich clusters, where galaxy velocities are typically much higher. This suggests that compact groups could be excellent laboratories in which to study galaxy interactions and their effects. Compact groups often contain one or more galaxies whose redshift differs greatly from those of the other group members. If these galaxies are at the same distance as the other members, either entire galaxies are being ejected at high velocities from these groups, or some new physical phenomena must be occurring. If their redshifts are cosmological, we must explain why so many discordant galaxies are found in compact groups. In recent years much progress has been made in addressing these questions. Here, the author discusses the current observational data on compact groups and their implications

The classification of 2-compact groups

DEFF Research Database (Denmark)

K. S. Andersen, Kasper; Grodal, Jesper

2009-01-01

with Moeller and Viruel for p odd, this establishes the full classification of p-compact groups, stating that, up to isomorphism, there is a one-to-one correspondence between connected p-compact groups and root data over the p-adic integers. As a consequence we prove the maximal torus conjecture, giving a one...

Density character of subgroups of topological groups

OpenAIRE

Leiderman, Arkady; Morris, Sidney A.; Tkachenko, Mikhail G.

2015-01-01

A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie groups which consists of projective limits of finite-dimensional Lie groups and proved that it contains all compact groups, locally compact abelian groups and connected locally compact groups and is closed under products and closed subgroups. A topological group...

An introduction to Lie groups and the geometry of homogeneous spaces

CERN Document Server

Arvanitoyeorgos, Andreas

2003-01-01

It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differenti...

Topological entropy of continuous actions of compactly generated groups

OpenAIRE

Schneider, Friedrich Martin

2015-01-01

We introduce a notion of topological entropy for continuous actions of compactly generated topological groups on compact Hausdorff spaces. It is shown that any continuous action of a compactly generated topological group on a compact Hausdorff space with vanishing topological entropy is amenable. Given an arbitrary compactly generated locally compact Hausdorff topological group $G$, we consider the canonical action of $G$ on the closed unit ball of $L^{1}(G)' \\cong L^{\\infty}(G)$ endowed with...

Harmonic analysis on exponential solvable Lie groups

CERN Document Server

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...

Algebras of Complete Hörmander Vector Fields, and Lie-Group Construction

Directory of Open Access Journals (Sweden)

Andrea Bonfiglioli

2014-12-01

Full Text Available The aim of this note is to characterize the Lie algebras g of the analytic vector fields in RN which coincide with the Lie algebras of the (analytic Lie groups defined on RN (with its usual differentiable structure. We show that such a characterization amounts to asking that: (i g is N-dimensional; (ii g admits a set of Lie generators which are complete vector fields; (iii g satisfies Hörmander’s rank condition. These conditions are necessary, sufficient and mutually independent. Our approach is constructive, in that for any such g we show how to construct a Lie group G = (RN, * whose Lie algebra is g. We do not make use of Lie’s Third Theorem, but we only exploit the Campbell-Baker-Hausdorff-Dynkin Theorem for ODE’s.

Lie Group Classifications and Non-differentiable Solutions for Time-Fractional Burgers Equation

International Nuclear Information System (INIS)

Wu Guocheng

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. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Co-compact Gabor Systems on Locally Compact Abelian Groups

DEFF Research Database (Denmark)

Jakobsen, Mads Sielemann; Lemvig, Jakob

2016-01-01

In this work we extend classical structure and duality results in Gabor analysis on the euclidean space to the setting of second countable locally compact abelian (LCA) groups. We formulate the concept of rationally oversampling of Gabor systems in an LCA group and prove corresponding characteriz...

Introduction to quantized LIE groups and algebras

International Nuclear Information System (INIS)

Tjin, T.

1992-01-01

In this paper, the authors give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups the authors study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then the authors explain in detail the concept of quantization for them. As an example the quantization of sl 2 is explicitly carried out. Next, the authors show how quantum groups are related to the Yang-Baxter equation and how they can be used to solve it. Using the quantum double construction, the authors explicitly construct the universal R matrix for the quantum sl 2 algebra. In the last section, the authors deduce all finite-dimensional irreducible representations for q a root of unity. The authors also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory

Trust and compactness in social network groups.

Science.gov (United States)

De Meo, Pasquale; Ferrara, Emilio; Rosaci, Domenico; Sarné, Giuseppe M L

2015-02-01

Understanding the dynamics behind group formation and evolution in social networks is considered an instrumental milestone to better describe how individuals gather and form communities, how they enjoy and share the platform contents, how they are driven by their preferences/tastes, and how their behaviors are influenced by peers. In this context, the notion of compactness of a social group is particularly relevant. While the literature usually refers to compactness as a measure to merely determine how much members of a group are similar among each other, we argue that the mutual trustworthiness between the members should be considered as an important factor in defining such a term. In fact, trust has profound effects on the dynamics of group formation and their evolution: individuals are more likely to join with and stay in a group if they can trust other group members. In this paper, we propose a quantitative measure of group compactness that takes into account both the similarity and the trustworthiness among users, and we present an algorithm to optimize such a measure. We provide empirical results, obtained from the real social networks EPINIONS and CIAO, that compare our notion of compactness versus the traditional notion of user similarity, clearly proving the advantages of our approach.

ENHANCED WARM H2 EMISSION IN THE COMPACT GROUP MID-INFRARED ''GREEN VALLEY''

International Nuclear Information System (INIS)

Cluver, M. E.; Ogle, P.; Guillard, P.; Appleton, P. N.; Jarrett, T. H.; Rasmussen, J.; Lisenfeld, U.; Verdes-Montenegro, L.; Antonucci, R.; Bitsakis, T.; Charmandaris, V.; Boulanger, F.; Egami, E.; Xu, C. K.; Yun, M. S.

2013-01-01

We present results from a Spitzer mid-infrared spectroscopy study of a sample of 74 galaxies located in 23 Hickson Compact Groups (HCGs), chosen to be at a dynamically active stage of H I depletion. We find evidence for enhanced warm H 2 emission (i.e., above that associated with UV excitation in star-forming regions) in 14 galaxies (∼20%), with 8 galaxies having extreme values of L(H 2 S(0)-S(3))/L(7.7 μm polycyclic aromatic hydrocarbon), in excess of 0.07. Such emission has been seen previously in the compact group HCG 92 (Stephan's Quintet), and was shown to be associated with the dissipation of mechanical energy associated with a large-scale shock caused when one group member collided, at high velocity, with tidal debris in the intragroup medium. Similarly, shock excitation or turbulent heating is likely responsible for the enhanced H 2 emission in the compact group galaxies, since other sources of heating (UV or X-ray excitation from star formation or active galactic nuclei) are insufficient to account for the observed emission. The group galaxies fall predominantly in a region of mid-infrared color-color space identified by previous studies as being connected to rapid transformations in HCG galaxy evolution. Furthermore, the majority of H 2 -enhanced galaxies lie in the optical ''green valley'' between the blue cloud and red sequence, and are primarily early-type disk systems. We suggest that H 2 -enhanced systems may represent a specific phase in the evolution of galaxies in dense environments and provide new insight into mechanisms which transform galaxies onto the optical red sequence.

Dynamics on the group manifolds and path integral

International Nuclear Information System (INIS)

Marinov, M.S.; Terentyev, M.V.

1979-01-01

Classical and quantum dynamics onn the compact simple Lie group and on the sphere of arbitrary dimensionality are considered. The accuracy of the semiclassical approximation for Green functions is discussed. Various path integral representations of the Green functions are presented. The special features of these representations due to the compactness and curvature are analysed. Basic results of the theory of Lie algebras and Lie groups used in the main text are presented

Definably compact groups definable in real closed fields. I

OpenAIRE

Barriga, Eliana

2017-01-01

We study definably compact definably connected groups definable in a sufficiently saturated real closed field $R$. We introduce the notion of group-generic point for $\\bigvee$-definable groups and show the existence of group-generic points for definably compact groups definable in a sufficiently saturated o-minimal expansion of a real closed field. We use this notion along with some properties of generic sets to prove that for every definably compact definably connected group $G$ definable in...

Application of Lie group analysis in geophysical fluid dynamics

CERN Document Server

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

Observability of linear control systems on Lie groups

International Nuclear Information System (INIS)

Ayala, V.; Hacibekiroglu, A.K.

1995-01-01

In this paper, we study the observability problem for a linear control system Σ on a Lie group G. The drift vector field of Σ is an infinitesimal automorphism of G and the control vectors are elements in the Lie algebra of G. We establish algebraic conditions to characterize locally and globally observability for Σ. As in the linear case on R n , these conditions are independent of the control vector. We give an algorithm on the co-tangent bundle of G to calculate the equivalence class of the neutral element. (author). 6 refs

Coherent states for quantum compact groups

CERN Document Server

Jurco, B

1996-01-01

Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the q--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}

Expansion in finite simple groups of Lie type

CERN Document Server

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 Lie based 4-dimensional higher Chern-Simons theory

Science.gov (United States)

Zucchini, Roberto

2016-05-01

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.

Differential calculus on quantized simple Lie groups

International Nuclear Information System (INIS)

Jurco, B.

1991-01-01

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q ε R are also discussed. (orig.)

Diagram Techniques in Group Theory

Science.gov (United States)

Stedman, Geoffrey E.

2009-09-01

Preface; 1. Elementary examples; 2. Angular momentum coupling diagram techniques; 3. Extension to compact simple phase groups; 4. Symmetric and unitary groups; 5. Lie groups and Lie algebras; 6. Polarisation dependence of multiphoton processes; 7. Quantum field theoretic diagram techniques for atomic systems; 8. Applications; Appendix; References; Indexes.

Canonical construction of differential operators intertwining representations of real semisimple Lie groups

International Nuclear Information System (INIS)

Dobrev, V.K.

1986-11-01

Let G be a real linear connected semisimple Lie group. We present a canonical construction of the differential operators intertwining elementary (≡ generalized principal series) representations of G. The results are easily extended to real linear reductive Lie groups. (author). 20 refs

The normal holonomy group

International Nuclear Information System (INIS)

Olmos, C.

1990-05-01

The restricted holonomy group of a Riemannian manifold is a compact Lie group and its representation on the tangent space is a product of irreducible representations and a trivial one. Each one of the non-trivial factors is either an orthogonal representation of a connected compact Lie group which acts transitively on the unit sphere or it is the isotropy representation of a single Riemannian symmetric space of rank ≥ 2. We prove that, all these properties are also true for the representation on the normal space of the restricted normal holonomy group of any submanifold of a space of constant curvature. 4 refs

Coherent states for quantum compact groups

International Nuclear Information System (INIS)

Jurco, B.; Stovicek, P.; CTU, Prague

1996-01-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A l , B l , C l and D l . The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)

Nature of compact groups of galaxies

International Nuclear Information System (INIS)

Hickson, P.; Rood, H.J.

1988-01-01

Monte Carlo numerical simulation is used to calculate the probability for the chance occurrence of four galaxies projected on the sky satisfying the Hickson isolation criterion within a loose group of eight members. For the models which match most closely the size and galaxy multiplicity function of observed groups, this chance occurrence is found to be smaller by a factor of about 100 than the value obtained previously by Mamom from numerical simulations of dynamical models of groups. This and other direct independent observational results from the literature constitute strong evidence that nearly all of the Hickson compact groups are real physical systems. It is concluded that the tendency for the spiral fraction of a compact group to be larger than the value inferred from the galaxy morphology-group density relation of rich clusters and loose groups is a real physical effect indicating that galaxy morphology depends strongly on a second parameter which, it is suggested, is the velocity dispersion of a system. 21 references

An Lp−Lq version of Hardy's theorem for spherical Fourier transform on semisimple Lie groups

Directory of Open Access Journals (Sweden)

S. Ben Farah

2004-01-01

Full Text Available We consider a real semisimple Lie group G with finite center and K a maximal compact subgroup of G. We prove an Lp−Lq version of Hardy's theorem for the spherical Fourier transform on G. More precisely, let a, b be positive real numbers, 1≤p, q≤∞, and f a K-bi-invariant measurable function on G such that ha−1f∈Lp(G and eb‖λ‖2ℱ(f∈Lq(+* (ha is the heat kernel on G. We establish that if ab≥1/4 and p or q is finite, then f=0 almost everywhere. If ab<1/4, we prove that for all p, q, there are infinitely many nonzero functions f and if ab=1/4 with p=q=∞, we have f=const ha.

Lie group classification and exact solutions of the generalized Kompaneets equations

Directory of Open Access Journals (Sweden)

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.

Poincare-Birkhoff-Witt theorems and generalized Casimir invariants for some infinite-dimensional Lie groups: II

International Nuclear Information System (INIS)

Ton-That, Tuong

2005-01-01

In a previous paper we gave a generalization of the notion of Casimir invariant differential operators for the infinite-dimensional Lie groups GL ∞ (C) (or equivalently, for its Lie algebra gj ∞ (C)). In this paper we give a generalization of the Casimir invariant differential operators for a class of infinite-dimensional Lie groups (or equivalently, for their Lie algebras) which contains the infinite-dimensional complex classical groups. These infinite-dimensional Lie groups, and their Lie algebras, are inductive limits of finite-dimensional Lie groups, and their Lie algebras, with some additional properties. These groups or their Lie algebras act via the generalized adjoint representations on projective limits of certain chains of vector spaces of universal enveloping algebras. Then the generalized Casimir operators are the invariants of the generalized adjoint representations. In order to be able to explicitly compute the Casimir operators one needs a basis for the universal enveloping algebra of a Lie algebra. The Poincare-Birkhoff-Witt (PBW) theorem gives an explicit construction of such a basis. Thus in the first part of this paper we give a generalization of the PBW theorem for inductive limits of Lie algebras. In the last part of this paper a generalization of the very important theorem in representation theory, namely the Chevalley-Racah theorem, is also discussed

Fock model and Segal-Bargmann transform for minimal representations of Hermitian Lie groups

DEFF Research Database (Denmark)

Hilgert, Joachim; Kobayashi, Toshiyuki; Möllers, Jan

2012-01-01

For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K_C-orbit X in p_C and the L^2-inner product involves a K-Bessel function as density. Here K is a maximal compact subgroup of G, and g......_C=k_C+p_C is a complexified Cartan decomposition. In this realization the space of k-finite vectors consists of holomorphic polynomials on X. The reproducing kernel of the Fock space is calculated explicitly in terms of an I-Bessel function. We further find an explicit formula of a generalized Segal-Bargmann transform which...... intertwines the Schroedinger and Fock model. Its kernel involves the same I-Bessel function. Using the Segal--Bargmann transform we also determine the integral kernel of the unitary inversion operator in the Schroedinger model which is given by a J-Bessel function....

Coherent states for quantum compact groups

Energy Technology Data Exchange (ETDEWEB)

Jurco, B. [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Stovicek, P. [Ceske Vysoke Uceni Technicke, Prague (Czech Republic). Dept. of Mathematics]|[CTU, Prague (Czech Republic). Doppler Inst.

1996-12-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A{sub l}, B{sub l}, C{sub l} and D{sub l}. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)

Differential calculus on quantized simple Lie groups

Energy Technology Data Exchange (ETDEWEB)

Jurco, B. (Dept. of Optics, Palacky Univ., Olomouc (Czechoslovakia))

1991-07-01

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU{sub q}(2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q {epsilon} R are also discussed. (orig.).

Analytic factorization of Lie group representations

DEFF Research Database (Denmark)

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....

Quantum dressing orbits on compact groups

Energy Technology Data Exchange (ETDEWEB)

Jurco, B. (Technische Univ. Clausthal, Clausthal-Zellerfeld (Germany). Sommerfeld Inst.); Stovicek, P. (Prague Univ. (Czechoslovakia). Dept. of Mathematics)

1993-02-01

The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decomposition in the general case. Quantum dressing orbits are describing explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient 'coherent states' are introduced and a correspondence between classical and quantum observables is given. (orig.).

Quantum dressing orbits on compact groups

International Nuclear Information System (INIS)

Jurco, B.; Stovicek, P.

1993-01-01

The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decomposition in the general case. Quantum dressing orbits are describing explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient 'coherent states' are introduced and a correspondence between classical and quantum observables is given. (orig.)

Mapping Spaces, Centralizers, and p-Local Finite Groups of Lie Type

DEFF Research Database (Denmark)

Laude, Isabelle

We study the space of maps from the classifying space of a finite p-group to theBorel construction of a finite group of Lie type G in characteristic p acting on itsbuilding. The first main result is a description of the homology with Fp-coefficients,showing that the mapping space, up to p...... between a finite p-group and theuncompleted classifying space of the p-local finite group coming from a finite groupof Lie type in characteristic p, providing some of the first results in this uncompletedsetting.......-completion, is a disjoint union indexedover the group homomorphism up to conjugation of classifying spaces of centralizersof p-subgroups in the underlying group G. We complement this description bydetermining the actual homotopy groups of the mapping space. These resultstranslate to descriptions of the space of maps...

Cluster X-varieties, amalgamation, and Poisson-Lie groups

DEFF Research Database (Denmark)

Fock, V. V.; Goncharov, A. B.

2006-01-01

In this paper, starting from a split semisimple real Lie group G with trivial center, we define a family of varieties with additional structures. We describe them as cluster χ-varieties, as defined in [FG2]. In particular they are Poisson varieties. We define canonical Poisson maps of these varie...

GLOBAL PROPERTIES OF NEUTRAL HYDROGEN IN COMPACT GROUPS

Energy Technology Data Exchange (ETDEWEB)

Walker, Lisa May [Steward Observatory, University of Arizona, Tucson, AZ 85721 (United States); Johnson, Kelsey E. [Department of Astronomy, University of Virginia, Charlottesville, VA 22904 (United States); Gallagher, Sarah C. [Department of Physics and Astronomy, University of Western Ontario, London, ON (Canada); Privon, George C. [Departamento de Astronomía, Universidad de Concepción, Concepción (Chile); Kepley, Amanda A. [National Radio Astronomy Observatory, Charlottesville, VA 22903 (United States); Whelan, David G. [Physics Department, Austin College, Sherman, TX 75090 (United States); Desjardins, Tyler D. [Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045 (United States); Zabludoff, Ann I. [Department of Astronomy and Steward Observatory, University of Arizona, Tucson, AZ 85721 (United States)

2016-02-15

Compact groups of galaxies provide a unique environment to study the evolution of galaxies amid frequent gravitational encounters. These nearby groups have conditions similar to those in the earlier universe when galaxies were assembled and give us the opportunity to witness hierarchical formation in progress. To understand how the compact group environment affects galaxy evolution, we examine the gas and dust in these groups. We present new single-dish GBT neutral hydrogen (H i) observations of 30 compact groups and define a new way to quantify the group H i content as the H i-to-stellar mass ratio of the group as a whole. We compare the H i content with mid-IR indicators of star formation and optical [g − r] color to search for correlations between group gas content and star formation activity of individual group members. Quiescent galaxies tend to live in H i-poor groups, and galaxies with active star formation are more commonly found in H i-rich groups. Intriguingly, we also find “rogue” galaxies whose star formation does not correlate with group H i content. In particular, we identify three galaxies (NGC 2968 in RSCG 34, KUG 1131+202A in RSCG 42, and NGC 4613 in RSCG 64) whose mid-IR activity is discrepant with the H i. We speculate that this mismatch between mid-IR activity and H i content is a consequence of strong interactions in this environment that can strip H i from galaxies and abruptly affect star formation. Ultimately, characterizing how and on what timescales the gas is processed in compact groups will help us understand the interstellar medium in complex, dense environments similar to the earlier universe.

GLOBAL PROPERTIES OF NEUTRAL HYDROGEN IN COMPACT GROUPS

International Nuclear Information System (INIS)

Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.; Privon, George C.; Kepley, Amanda A.; Whelan, David G.; Desjardins, Tyler D.; Zabludoff, Ann I.

2016-01-01

Compact groups of galaxies provide a unique environment to study the evolution of galaxies amid frequent gravitational encounters. These nearby groups have conditions similar to those in the earlier universe when galaxies were assembled and give us the opportunity to witness hierarchical formation in progress. To understand how the compact group environment affects galaxy evolution, we examine the gas and dust in these groups. We present new single-dish GBT neutral hydrogen (H i) observations of 30 compact groups and define a new way to quantify the group H i content as the H i-to-stellar mass ratio of the group as a whole. We compare the H i content with mid-IR indicators of star formation and optical [g − r] color to search for correlations between group gas content and star formation activity of individual group members. Quiescent galaxies tend to live in H i-poor groups, and galaxies with active star formation are more commonly found in H i-rich groups. Intriguingly, we also find “rogue” galaxies whose star formation does not correlate with group H i content. In particular, we identify three galaxies (NGC 2968 in RSCG 34, KUG 1131+202A in RSCG 42, and NGC 4613 in RSCG 64) whose mid-IR activity is discrepant with the H i. We speculate that this mismatch between mid-IR activity and H i content is a consequence of strong interactions in this environment that can strip H i from galaxies and abruptly affect star formation. Ultimately, characterizing how and on what timescales the gas is processed in compact groups will help us understand the interstellar medium in complex, dense environments similar to the earlier universe

Quantization and harmonic analysis on nilpotent Lie groups

International Nuclear Information System (INIS)

Wildberger, N.J.

1983-01-01

Weyl Quantization is a procedure for associating a function on which the canonical commutation relations are realized. If G is a simply-connected, connected nilpotent Lie group with Lie algebra g and dual g/sup */, it is shown how to inductively construct symplectic isomorphisms between every co-adjoint orbit O and the bundle in Hilbert Space for some m. Weyl Quantization can then be used to associate to each orbit O a unitary representation rho 0 of G, recovering the classification of the unitary dual by Kirillov. It is used to define a geometric Fourier transform, F : L 1 (G) → functions on g/sup */, and it is shown that the usual operator-valued Fourier transform can be recovered from F, characters are inverse Fourier transforms of invariant measures on orbits, and matrix coefficients are inverse Fourier transforms of non-invariant measures supported on orbits. Realizations of the representations rho 0 in subspaces of L 2 (O) are obtained.. Finally, the kernel function is computed for the upper triangular unipotent group and one other example

Topological Poisson Sigma models on Poisson-Lie groups

International Nuclear Information System (INIS)

Calvo, Ivan; Falceto, Fernando; Garcia-Alvarez, David

2003-01-01

We solve the topological Poisson Sigma model for a Poisson-Lie group G and its dual G*. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of both models in the open geometry reveals that there exists a map from the reduced phase of each model (P and P*) to the main symplectic leaf of the Heisenberg double (D 0 ) such that the symplectic forms on P, P* are obtained as the pull-back by those maps of the symplectic structure on D 0 . This uncovers a duality between P and P* under the exchange of bulk degrees of freedom of one model with boundary degrees of freedom of the other one. We finally solve the Poisson Sigma model for the Poisson structure on G given by a pair of r-matrices that generalizes the Poisson-Lie case. The Hamiltonian analysis of the theory requires the introduction of a deformation of the Heisenberg double. (author)

Definably compact groups definable in real closed fields.II

OpenAIRE

Barriga, Eliana

2017-01-01

We continue the analysis of definably compact groups definable in a real closed field $\\mathcal{R}$. In [3], we proved that for every definably compact definably connected semialgebraic group $G$ over $\\mathcal{R}$ there are a connected $R$-algebraic group $H$, a definable injective map $\\phi$ from a generic definable neighborhood of the identity of $G$ into the group $H\\left(R\\right)$ of $R$-points of $H$ such that $\\phi$ acts as a group homomorphism inside its domain. The above result and o...

LIE GROUPS AND NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS: INVARIANT DISCRETIZATION VERSUS DIFFERENTIAL APPROXIMATION

Directory of Open Access Journals (Sweden)

Decio Levi

2013-10-01

Full Text Available We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which the “first differential approximation” is invariant under the same Lie group as the original ordinary differential equation.

Fourier-like frames on locally compact abelian groups

DEFF Research Database (Denmark)

Christensen, Ole; Goh, Say Song

2015-01-01

We consider a class of functions, defined on a locally compact abelian group by letting a class of modulation operators act on a countable collection of functions. We derive sufficient conditions for such a class of functions to form a Bessel sequence or a frame and for two such systems to be dual...... frames. Explicit constructions are obtained via various generalizations of the classical B-splines to the setting of locally compact abelian groups. (C) 2014 Elsevier Inc. All rights reserved....

Are There Limits to Collectivism? Culture and Children's Reasoning About Lying to Conceal a Group Transgression.

Science.gov (United States)

Sweet, Monica A; Heyman, Gail D; Fu, Genyue; Lee, Kang

2010-07-01

This study explored the effects of collectivism on lying to conceal a group transgression. Seven-, 9-, and 11-year-old US and Chinese children (N = 374) were asked to evaluate stories in which protagonists either lied or told the truth about their group's transgression and were then asked about either the protagonist's motivations or justification for their own evaluations. Previous research suggests that children in collectivist societies such as China find lying for one's group to be more acceptable than do children from individualistic societies such as the United States. The current study provides evidence that this is not always the case: Chinese children in this study viewed lies told to conceal a group's transgressions less favourably than did US children. An examination of children's reasoning about protagonists' motivations for lying indicated that children in both countries focused on an impact to self when discussing motivations for protagonists to lie for their group. Overall, results suggest that children living in collectivist societies do not always focus on the needs of the group.

Exceptional Lie groups, E-infinity theory and Higgs Boson

International Nuclear Information System (INIS)

El-Okaby, Ayman A.

2008-01-01

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

Perturbative expansion of Chern-Simons theory with non-compact gauge group

International Nuclear Information System (INIS)

Bar-Natan, D.; Witten, E.

1991-01-01

Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly 'unitary' format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified. (orig.)

Some New Lie Symmetry Groups of Differential-Difference Equations Obtained from a Simple Direct Method

International Nuclear Information System (INIS)

Zhi Hongyan

2009-01-01

In this paper, based on the symbolic computing system Maple, the direct method for Lie symmetry groups presented by Sen-Yue Lou [J. Phys. A: Math. Gen. 38 (2005) L129] is extended from the continuous differential equations to the differential-difference equations. With the extended method, we study the well-known differential-difference KP equation, KZ equation and (2+1)-dimensional ANNV system, and both the Lie point symmetry groups and the non-Lie symmetry groups are obtained.

Bicovariant quantum algebras and quantum Lie algebras

International Nuclear Information System (INIS)

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

1993-01-01

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

Lie algebras

CERN Document Server

Jacobson, Nathan

1979-01-01

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

On the absence of order in 2-dimensional systems with compact symmetry

International Nuclear Information System (INIS)

Bruschi, M.L.; Garcia, A.A.; Masperi, L.; Garcia Canal, C.A.

1984-01-01

An alternative proof for the generalization to any compact Lie group of the absence of an ordered phase in one and two dimensional classical systems is provided using the original Bogoliubov inequality. (Author) [pt

Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras

NARCIS (Netherlands)

Put, Marius van der

1999-01-01

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

Construction of Difference Equations Using Lie Groups

International Nuclear Information System (INIS)

Axford, R.A.

1998-01-01

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

Non-Supramenable Groups Acting on Locally Compact Spaces

DEFF Research Database (Denmark)

Kellerhals, Julian; Monod, Nicolas; Rørdam, Mikael

2013-01-01

Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product $C^*$-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UCT class are constructed using crossed ...

Invariance Lie algebra and group of the non relativistic hydrogen atom

International Nuclear Information System (INIS)

Decoster, Alain

1970-01-01

The first part of this work contains a general survey of the use of Lie groups and algebras in quantum mechanics, followed by an extensive description of tbe invariance algebra and invariance group of the non-relativistic hydrogen atom; the realization of this group discovered by FOCK is specially examined. The second part is a two-hundred items bibliography on invariance groups and algebras of classical and quantum-mechanical simple systems. (author) [fr

Lie superalgebras

International Nuclear Information System (INIS)

Berezin, F.A.

1977-01-01

Generalization of the Laplace-Casimir operator theory on the Lie supergroups is considered. The main result is the formula for radial parts of the Laplace operators under some general assumptions about the Lie supergroup. In particular these assumptions are valid for the Lie suppergroups U(p,g) and C (m,n). The first one is the analogue of the unitary group, the second one is the analogue of the linear group of canonical transformations

A density matrix renormalization group study of low-lying excitations ...

Indian Academy of Sciences (India)

Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited 2 symmetry and spin parity of the system to obtain excited states of ...

On E-discretization of tori of compact simple Lie groups. II

Science.gov (United States)

Hrivnák, Jiří; Juránek, Michal

2017-10-01

Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.

International Workshop "Groups, Rings, Lie and Hopf Algebras"

CERN Document Server

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.

Group actions, non-Kähler complex manifolds and SKT structures

Directory of Open Access Journals (Sweden)

Poddar Mainak

2018-02-01

Full Text Available We give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler complex structures on tangential frame bundles of complex orbifolds.

Koszul information geometry and Souriau Lie group thermodynamics

Energy Technology Data Exchange (ETDEWEB)

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].

On the structure of finite-sheeted coverings of compact connected groups

OpenAIRE

Grigorian, S. A.; Gumerov, R. N.

2004-01-01

Finite-sheeted covering mappings onto compact connected groups are studied. It is shown that a finite-sheeted covering mapping from a connected Hausdorff topological space onto a compact connected abelian group G must be a homeomorphism provided that the character group of G admits division by the degree of given covering mapping. Using this result, we obtain criteria of triviality for finite coverings of G in terms of its character group and means on G. In order to establish these facts, for...

EXAMINING THE ROLE OF ENVIRONMENT IN A COMPREHENSIVE SAMPLE OF COMPACT GROUPS

International Nuclear Information System (INIS)

Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.; Charlton, Jane C.; Hornschemeier, Ann E.; Hibbard, John E.

2012-01-01

Compact groups, with their high number densities, small velocity dispersions, and an interstellar medium that has not been fully processed, provide a local analog to conditions of galaxy interactions in the earlier universe. The frequent and prolonged gravitational encounters that occur in compact groups affect the evolution of the constituent galaxies in a myriad of ways, for example, gas processing and star formation. Recently, a statistically significant 'gap' has been discovered in the mid-infrared (MIR: 3.6-8 μm) IRAC color space of compact group galaxies. This gap is not seen in field samples and is a new example of how the compact group environment may affect the evolution of member galaxies. In order to investigate the origin and nature of this gap, we have compiled a larger sample of 37 compact groups in addition to the original 12 groups studied by Johnson et al. (yielding 174 individual galaxies with reliable MIR photometry). We find that a statistically significant deficit of galaxies in this gap region of IRAC color space is persistent in the full sample, lending support to the hypothesis that the compact group environment inhibits moderate specific star formation rates. Using this expanded sample, we have more fully characterized the distribution of galaxies in this color space and quantified the low-density region more fully with respect to MIR bluer and MIR redder colors. We note a curvature in the color-space distribution, which is fully consistent with increasing dust temperature as the activity in a galaxy increases. This full sample of 49 compact groups allows us to subdivide the data according to physical properties of the groups. An analysis of these subsamples indicates that neither projected physical diameter nor density shows a trend in color space within the values represented by this sample. We hypothesize that the apparent lack of a trend is due to the relatively small range of properties in this sample, whose groups have already been

Examining the Role of Environment in a Comprehensive Sample of Compact Groups

Science.gov (United States)

Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.; Charlton, Jane C.; Hornschemeier, Ann E.; Hibbard, John E.

2012-03-01

Compact groups, with their high number densities, small velocity dispersions, and an interstellar medium that has not been fully processed, provide a local analog to conditions of galaxy interactions in the earlier universe. The frequent and prolonged gravitational encounters that occur in compact groups affect the evolution of the constituent galaxies in a myriad of ways, for example, gas processing and star formation. Recently, a statistically significant "gap" has been discovered in the mid-infrared (MIR: 3.6-8 μm) IRAC color space of compact group galaxies. This gap is not seen in field samples and is a new example of how the compact group environment may affect the evolution of member galaxies. In order to investigate the origin and nature of this gap, we have compiled a larger sample of 37 compact groups in addition to the original 12 groups studied by Johnson et al. (yielding 174 individual galaxies with reliable MIR photometry). We find that a statistically significant deficit of galaxies in this gap region of IRAC color space is persistent in the full sample, lending support to the hypothesis that the compact group environment inhibits moderate specific star formation rates. Using this expanded sample, we have more fully characterized the distribution of galaxies in this color space and quantified the low-density region more fully with respect to MIR bluer and MIR redder colors. We note a curvature in the color-space distribution, which is fully consistent with increasing dust temperature as the activity in a galaxy increases. This full sample of 49 compact groups allows us to subdivide the data according to physical properties of the groups. An analysis of these subsamples indicates that neither projected physical diameter nor density shows a trend in color space within the values represented by this sample. We hypothesize that the apparent lack of a trend is due to the relatively small range of properties in this sample, whose groups have already been

Global dimensions for Lie groups at level k and their conformally exceptional quantum subgroups

CERN Document Server

Coquereaux, Robert

2010-01-01

We obtain formulae giving global dimensions for fusion categories defined by Lie groups G at level k and for the associated module-categories obtained via conformal embeddings. The results can be expressed in terms of Lie quantum superfactorials of type G. The later are related, for the type Ar, to the quantum Barnes function.

ROSAT: X ray survey of compact groups

NARCIS (Netherlands)

van Gorkom, Jacqueline

1993-01-01

This is the final technical report on grant NAG5-1954, which was awarded under the NASA ROSAT Guest Investigator Program to Columbia University. This grant was awarded for a number of projects on two rather different topics: (1) an x-ray survey of compact groups of galaxies; and (2) the fate of gas

Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups

OpenAIRE

Beltita, Ingrid; Beltita, Daniel

2009-01-01

We present some recent results on smooth vectors for unitary irreducible representations of nilpotent Lie groups. Applications to the Weyl-Pedersen calculus of pseudo-differential operators with symbols on the coadjoint orbits are also discussed.

Factorial representations of path groups

International Nuclear Information System (INIS)

Albeverio, S.; Hoegh-Krohn, R.; Testard, D.; Vershik, A.

1983-11-01

We give the reduction of the energy representation of the group of mappings from I = [ 0,1 ], S 1 , IRsub(+) or IR into a compact semi simple Lie group G. For G = SU(2) we prove the factoriality of the representation, which is of type III in the case I = IR

Automorphic Lie algebras with dihedral symmetry

International Nuclear Information System (INIS)

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

2014-01-01

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

Motivation and Consequences of Lying. A Qualitative Analysis of Everyday Lying

Directory of Open Access Journals (Sweden)

Beata Arcimowicz

2015-09-01

Full Text Available This article presents findings of qualitative analysis of semi-structured interviews with a group of "frequent liars" and another of "rare liars" who provided their subjective perspectives on the phenomenon of lying. Participants in this study previously had maintained a diary of their social interactions and lies over the course of one week, which allowed to assign them to one of the two groups: frequent or rare liars. Thematic analysis of the material followed by elements of theory formulation resulted in an extended lying typology that includes not only the target of the lie (the liar vs. other but also the motivation (protection vs. bringing benefits. We offer an analysis of what prevents from telling the truth, i.e. penalties, relationship losses, distress of the lied-to, and anticipated lack of criticism for telling the truth. We also focus on understanding moderatorsof consequences of lying (significance of the area of life, the type of lie and capacity to understand the liar that can be useful in future studies. URN: http://nbn-resolving.de/urn:nbn:de:0114-fqs1503318

Control Algorithms Along Relative Equilibria of Underactuated Lagrangian Systems on Lie Groups

DEFF Research Database (Denmark)

Nordkvist, Nikolaj; Bullo, F.

2008-01-01

We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation...

Control algorithms along relative equilibria of underactuated Lagrangian systems on Lie groups

DEFF Research Database (Denmark)

Nordkvist, Nikolaj; Bullo, Francesco

2007-01-01

We present novel algorithms to control underactuated mechanical systems. For a class of invariant systems on Lie groups, we design iterative small-amplitude control forces to accelerate along, decelerate along, and stabilize relative equilibria. The technical approach is based upon a perturbation...

Free Fermions and the Classical Compact Groups

Science.gov (United States)

Cunden, Fabio Deelan; Mezzadri, Francesco; O'Connell, Neil

2018-06-01

There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.

Free Fermions and the Classical Compact Groups

Science.gov (United States)

Cunden, Fabio Deelan; Mezzadri, Francesco; O'Connell, Neil

2018-04-01

There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.

Quantum spaces, central extensions of Lie groups and related quantum field theories

Science.gov (United States)

Poulain, Timothé; Wallet, Jean-Christophe

2018-02-01

Quantum spaces with su(2) noncommutativity can be modelled by using a family of SO(3)-equivariant differential *-representations. The quantization maps are determined from the combination of the Wigner theorem for SU(2) with the polar decomposition of the quantized plane waves. A tracial star-product, equivalent to the Kontsevich product for the Poisson manifold dual to su(2) is obtained from a subfamily of differential *-representations. Noncommutative (scalar) field theories free from UV/IR mixing and whose commutative limit coincides with the usual ϕ 4 theory on ℛ3 are presented. A generalization of the construction to semi-simple possibly non simply connected Lie groups based on their central extensions by suitable abelian Lie groups is discussed. Based on a talk presented by Poulain T at the XXVth International Conference on Integrable Systems and Quantum symmetries (ISQS-25), Prague, June 6-10 2017.

The Exceptional Lie symmetry groups hierarchy and the expected number of Higgs bosons

International Nuclear Information System (INIS)

El Naschie, M.S.

2008-01-01

New insights into the structure of various exceptional Lie symmetry groups hierarchies are utilized to shed light on various problems pertinent to the standard model of high energy physics and the Higgs

On the Chabauty space of locally compact abelian groups

OpenAIRE

Cornulier, Yves

2010-01-01

This paper contains several results about the Chabauty space of a general locally compact abelian group. Notably, we determine its topological dimension, we characterize when it is totally disconnected or connected; we characterize isolated points.

Group formalism of Lie transformations to time-fractional partial ...

Indian Academy of Sciences (India)

Lie symmetry analysis; Fractional partial differential equation; Riemann–Liouville fractional derivative ... science and engineering. It is known that while ... differential equations occurring in different areas of applied science [11,14]. The Lie ...

Photometric observations of nine Shakhbazian compact groups

International Nuclear Information System (INIS)

Tovmassian, H.M.; Tiersch, H.; Tovmassian, G.H.; Neizvestny, S.

2010-01-01

By observations with the 1.5m telescope at San Pedro Martir (OAN, UNAM, Mexico) the BVR magnitudes are determined for 66 member galaxies in Shakhbazian Compact Galaxy Groups ShCG 40, ShCG 176, ShCG 270, ShCG 278, ShCG 310 and ShCG 342. Three other groups were observed in two or only in one band. Seven galaxies in ShCG 298 were observed in B and R, six galaxies in ShCG 95 were observed in V and 7 galaxies in ShCG 345 were observed in V and R. The distribution of brightness of observed galaxies is determined. Signs of interaction between galaxies are detected in some groups

Group C∗-algebras without the completely bounded approximation property

DEFF Research Database (Denmark)

Haagerup, U.

2016-01-01

It is proved that: (1) The Fourier algebra A(G) of a simple Lie group G of real rank at least 2 with finite center does not have a multiplier bounded approximate unit. (2) The reduced C∗-algebra C∗ r of any lattice in a non-compact simple Lie group of real rank at least 2 with finite center does...... not have the completely bounded approximation property. Hence, the results obtained by de Canniere and the author for SOe (n, 1), n ≥ 2, and by Cowling for SU(n, 1) do not generalize to simple Lie groups of real rank at least 2. © 2016 Heldermann Verlag....

Introduction to compact (matrix) quantum groups and Banica ...

Indian Academy of Sciences (India)

Moritz Weber

2017-11-27

Nov 27, 2017 ... Building on this, we define Banica–Speicher quantum .... four vertices) are ... A compact Hausdorff space X gives rise to a commutative unitalC .... (a) Recall the construction of the group C ..... Having formulated the features of the Haar integration in 'quantum terms', ...... paper: When is the map in [30, Prop.

Lie groups, differential equations, and geometry advances and surveys

CERN Document Server

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.

Global solvability of the differential operators non-invariants on semi-simple Lie groups

International Nuclear Information System (INIS)

El Hussein, K.

1991-09-01

Let G be a connected semi-simple Lie group with finite centre and let G=KAN be the Iwasawa decomposition of G. Let P be a differential operator on G, which is right invariant by the sub-group AN and left invariant by the sub-group K. In this paper, we give a necessary and sufficient condition for the global solvability of P on G. (author). 5 refs

Limits of commutative triangular systems on locally compact groups

Indian Academy of Sciences (India)

Commutative triangular systems of probability measures on locally compact groups have been studied extensively and ... in [S3,S4], we extend our earlier result to some particular triangular systems on algebraic groups. We also discuss ..... Now G can be embedded as a closed subgroup in. G2 ¼ G1=D and G0. 2 ¼ ًG0 آ ...

Analytic vectors and irreducible representations of nilpotent Lie groups and algebras

International Nuclear Information System (INIS)

Arnal, D.

1978-01-01

Let U be a unitary irreducible locally faithful representation of a nilpotent Lie group G, V the universal enveloping algebra of G, M a simple module on V with kernel ker dU, then there exists an automorphism of V keeping ker dU invariant such that, after transport of structure, M is isomorphic to a submodule of the space of analytic vectors for U. (Auth.)

Bounds on the number of possible Higgs particles using grand unification and exceptional Lie groups

International Nuclear Information System (INIS)

El Naschie, M.S.

2008-01-01

The total sum of dimensions of a magnum exceptional Lie symmetry groups hierarchy is 4α-bar o =(4)(137+k o )≅548. Dividing this value among the various quantum fields leads to the possibility of an eight degrees of freedom Higgs field. However analyzing the same situation using sub groups of the largest exceptional Lie group leads to the conclusion that we are likely to find three Higgs particles only at the energy scale of the standard model. Consequently five of the eight degrees of freedom are unlikely to materialize as particles at this particular energy scale. This conclusion is reinforced by an entirely different approach based on grand unification analysis which excludes any grand unification using 4HD, i.e. four Higgs doublets. This leaves us with one, two and three Higgs doublets. Noting that a super symmetric standard model with two Higgs doublets gives almost perfect grand unification and that the result agrees with our exceptional Lie symmetry groups analysis, we exclude everything else. The final result is that we expect to find at least three more Higgs particles leading to a total of 66 elementary particles while at a somewhat higher energy, the expected number of 69 particles found using E-infinity theory is obtained

Dynamical properties of compact groups of galaxies

Science.gov (United States)

Hickson, Paul; De Oliveira, Claudia M.; Huchra, John P.; Palumbo, Giorgio G.

1992-01-01

Radial velocities are presented for 457 galaxies in the 100 Hickson compact groups. More than 84 percent of the galaxies measured have velocities within 1000 km/s of the median velocity in the group. Ninety-two groups have at least three accordant members, and 69 groups have at least four. The radial velocities of these groups range from 1380 to 42,731 km/s with a median of 8889 km/s, corresponding to a median distance of 89/h Mpc. The apparent space density of these systems ranges from 300 to as much as 10 exp 8 sq h/sq Mpc, which exceeds the densities in the centers of rich clusters. The median projected separation between galaxies is 39/h kpc, comparable to the sizes of the galaxies themselves. A significant correlation is found between crossing time and the fraction of gas-rich galaxies in the groups, and a weak anticorrelation is found between crossing time and the luminosity contrast of the first-ranked galaxy.

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

International Nuclear Information System (INIS)

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

1999-04-01

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

Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras

Directory of Open Access Journals (Sweden)

Meer Ashwinkumar

2018-03-01

Full Text Available We study the ground states and left-excited states of the Ak−1 N=(2,0 little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU(k. The ground states, described by L2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.

Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras

Science.gov (United States)

Ashwinkumar, Meer; Cao, Jingnan; Luo, Yuan; Tan, Meng-Chwan; Zhao, Qin

2018-03-01

We study the ground states and left-excited states of the Ak-1 N = (2 , 0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU (k). The ground states, described by L2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.

MID-INFRARED EVIDENCE FOR ACCELERATED EVOLUTION IN COMPACT GROUP GALAXIES

International Nuclear Information System (INIS)

Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.; Hibbard, John E.; Hornschemeier, Ann E.; Tzanavaris, Panayiotis; Charlton, Jane C.; Jarrett, Thomas H.

2010-01-01

Compact galaxy groups are at the extremes of the group environment, with high number densities and low velocity dispersions that likely affect member galaxy evolution. To explore the impact of this environment in detail, we examine the distribution in the mid-infrared (MIR) 3.6-8.0 μm color space of 42 galaxies from 12 Hickson compact groups (HCGs) in comparison with several control samples, including the LVL+SINGS galaxies, interacting galaxies, and galaxies from the Coma Cluster. We find that the HCG galaxies are strongly bimodal, with statistically significant evidence for a gap in their distribution. In contrast, none of the other samples show such a marked gap, and only galaxies in the Coma infall region have a distribution that is statistically consistent with the HCGs in this parameter space. To further investigate the cause of the HCG gap, we compare the galaxy morphologies of the HCG and LVL+SINGS galaxies, and also probe the specific star formation rate (SSFR) of the HCG galaxies. While galaxy morphology in HCG galaxies is strongly linked to position with MIR color space, the more fundamental property appears to be the SSFR, or star formation rate normalized by stellar mass. We conclude that the unusual MIR color distribution of HCG galaxies is a direct product of their environment, which is most similar to that of the Coma infall region. In both cases, galaxy densities are high, but gas has not been fully processed or stripped. We speculate that the compact group environment fosters accelerated evolution of galaxies from star-forming and neutral gas-rich to quiescent and neutral gas-poor, leaving few members in the MIR gap at any time.

Lie bialgebras with triangular decomposition

International Nuclear Information System (INIS)

Andruskiewitsch, N.; Levstein, F.

1992-06-01

Lie bialgebras originated in a triangular decomposition of the underlying Lie algebra are discussed. The explicit formulas for the quantization of the Heisenberg Lie algebra and some motion Lie algebras are given, as well as the algebra of rational functions on the quantum Heisenberg group and the formula for the universal R-matrix. (author). 17 refs

Dual Solutions for Nonlinear Flow Using Lie Group Analysis.

Directory of Open Access Journals (Sweden)

Muhammad Awais

Full Text Available `The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD flow of an upper-convected Maxwell (UCM fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered.

Unipotent and nilpotent classes in simple algebraic groups and lie algebras

CERN Document Server

Liebeck, Martin W

2012-01-01

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

A diagram approach to character formulae for finite and compact groups

International Nuclear Information System (INIS)

Kibler, M.; Elbaz, E.

1978-06-01

Some basic relations for the representation theory and the Wigner-Racah algebra of a finite or compact continuous group are discussed and transcribed in terms of diagrams. Special emphasis is placed on the case of a simply reducible group and all the diagrams are applicable to SU 2 without any change

Renormalization group flows and continual Lie algebras

International Nuclear Information System (INIS)

Bakas, Ioannis

2003-01-01

We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by (d/dt;1), with anti-symmetric Cartan kernel K(t,t') = δ'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N vertical bar N+1) in the large-N limit. 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, t. We provide the general solution of the renormalization group flows in terms of free fields, via Baecklund 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, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra (d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown. (author)

Modulus of smoothness and theorems concerning approximation on compact groups

Directory of Open Access Journals (Sweden)

H. Vaezi

2003-01-01

Full Text Available We consider the generalized shift operator defined by (Shuf(g=∫Gf(tut−1gdt on a compact group G, and by using this operator, we define “spherical” modulus of smoothness. So, we prove Stechkin and Jackson-type theorems.

The Merger History, AGN and Dwarf Galaxies of Hickson Compact Group 59

Science.gov (United States)

Konstantopoulos, I. S.; Gallagher, S. C.; Fedotov, K.; Durrell, P. R.; Tzanavaris, P.; Hill, A. R.; Zabludoff, A. I.; Maier, M. L.; Elmegreen, D. M.; Charlton, J. C.;

Bismut's way of the Malliavin calculus for large order generators on a Lie group

Science.gov (United States)

Léandre, Rémi

2018-01-01

We adapt Bismut's mechanism of the Malliavin Calculus to right invariant big order generator on a Lie group. We use deeply the symmetry in order to avoid the use of the Malliavin matrix. As an application, we deduce logarithmic estimates in small time of the heat kernel.

Isometric coactions of compact quantum groups on compact ...

Indian Academy of Sciences (India)

a compact quantum metric space in the framework of Rieffel, where the ... This problem can be formulated and studied in various settings. ... The spaces we are interested in this paper are metric spaces, both classical and quantum. ... He has given a definition for a quantum symmetry of a classical ...... by the construction of I.

Cartan determinants, LIE algebra extensions, and the exceptional group series

International Nuclear Information System (INIS)

Capps, R.H.

1986-01-01

In this note the author utilizes the determinant of the generalized Cartan matrix for candidate Dynkin systems for two purposes. The first is to provide an uncomplicated criterion for classifying candidate one-root extensions of diagrams for semisimple Lie algebras. The second is to help determine some important properties of related Lie algebras and their representations

Exponentiation and deformations of Lie-admissible algebras

International Nuclear Information System (INIS)

Myung, H.C.

1982-01-01

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

On the Lie symmetry group for classical fields in noncommutative space

Energy Technology Data Exchange (ETDEWEB)

Pereira, Ricardo Martinho Lima Santiago [Universidade Federal da Bahia (UFBA), BA (Brazil); Instituto Federal da Bahia (IFBA), BA (Brazil); Ressureicao, Caio G. da [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica; Vianna, Jose David M. [Universidade Federal da Bahia (UFBA), BA (Brazil); Universidade de Brasilia (UnB), DF (Brazil)

2011-07-01

Full text: An alternative way to include effects of noncommutative geometries in field theory is based on the concept of noncommutativity among degrees of freedom of the studied system. In this context it is reasonable to consider that, in the multiparticle noncommutative quantum mechanics (NCQM), the noncommutativity among degrees of freedom to discrete system with N particles is also verified. Further, an analysis of the classical limit of the single particle NCQM leads to a deformed Newtonian mechanics where the Newton's second law is modified in order to include the noncommutative parameter {theta}{sub {iota}j} and, for a one-dimensional discrete system with N particles, the dynamical evolution of each particle is given by this modified Newton's second law. Hence, applying the continuous limit to this multiparticle classical system it is possible to obtain a noncommutative extension of two -dimensional field theory in a noncommutative space. In the present communication we consider a noncommutative extension of the scalar field obtained from this approach and we analyze the Lie symmetries in order to compare the Lie group of this field with the usual scalar field in the commutative space. (author)

Lie Group Analysis of the Photo-Induced Fluorescence of Drosophila Oogenesis with the Asymmetrically Localized Gurken Protein.

Directory of Open Access Journals (Sweden)

Jen-Cheng Wang

Full Text Available Lie group analysis of the photo-induced fluorescence of Drosophila oogenesis with the asymmetrically localized Gurken protein has been performed systematically to assess the roles of ligand-receptor complexes in follicle cells. The (2×2 matrix representations resulting from the polarized tissue spectra were employed to characterize the asymmetrical Gurken distributions. It was found that the fluorescence of the wild-type egg shows the Lie point symmetry X 23 at early stages of oogenesis. However, due to the morphogen regulation by intracellular proteins and extracellular proteins, the fluorescence of the embryogenesis with asymmetrically localized Gurken expansions exhibits specific symmetry features: Lie point symmetry Z 1 and Lie point symmetry X 1. The novel approach developed herein was successfully used to validate that the invariant-theoretical characterizations are consonant with the observed asymmetric fluctuations during early embryological development.

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

OpenAIRE

Jurco, Branislav

2011-01-01

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

Geometric Theory of Heat from Souriau Lie Groups Thermodynamics and Koszul Hessian Geometry: Applications in Information Geometry for Exponential Families

Directory of Open Access Journals (Sweden)

Frédéric Barbaresco

2016-11-01

Full Text Available We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using geometric Planck temperature of Souriau model and symplectic cocycle notion, the Fisher metric is identified as a Souriau geometric heat capacity. The Souriau model is based on affine representation of Lie group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie group thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant–Kirillov–Souriau 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of information geometry for the action of an affine group for exponential families, and provide some illustrations of use cases for multivariate gaussian densities. Information geometry is presented in the context of the seminal work of Fréchet and his Clairaut-Legendre equation. The Souriau model of statistical physics is validated as compatible with the Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

Quantum group symmetry of classical and noncommutative geometry

Indian Academy of Sciences (India)

Debashish Goswami

2016-07-01

Jul 1, 2016 ... universal enveloping algebra U(L) of a Lie algebra L, (iv) ... Kustermans defined locally compact quantum groups too. .... There are other versions of quantum isometries formulated by me ..... classical connected spaces when either the space is ..... Etingof-Walton's paper, we have : (i) M0 is open and dense,.

Compact Information Representations

Science.gov (United States)

2016-08-02

Department of Defense, Executive Services, Directorate (0704-0188).   Respondents should be aware that notwithstanding any other provision of law, no person...which lies in the mission of AFOSR. 15.  SUBJECT TERMS sparse sampling , principal components analysis 16.  SECURITY CLASSIFICATION OF: 17...approved for public release Contents 1 Training for Ph.D. Students and Postdoc Researchers 2 2 Papers 2 3 Summary of Proposed Research: Compact

Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids

International Nuclear Information System (INIS)

Holm, D.D.

1976-07-01

The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented

Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids

Energy Technology Data Exchange (ETDEWEB)

Holm, D.D.

1976-07-01

The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented.

A Third-Order p-Laplacian Boundary Value Problem Solved by an SL(3,ℝ Lie-Group Shooting Method

Directory of Open Access Journals (Sweden)

Chein-Shan Liu

2013-01-01

Full Text Available The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP. In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,ℝ. Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can iteratively solve the missing left boundary conditions, which are determined by matching the right boundary conditions through a finer tuning of r∈[0,1]. The present SL(3,ℝ Lie-group shooting method is easily implemented and is efficient to tackle the multiple solutions of the third-order p-Laplacian. When the missing left boundary values can be determined accurately, we can apply the fourth-order Runge-Kutta (RK4 method to obtain a quite accurate numerical solution of the p-Laplacian.

Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions

Directory of Open Access Journals (Sweden)

Motlatsi Molati

2012-01-01

Full Text Available The aim of this work is to perform a complete Lie symmetry classification of a generalized Lane-Emden type system in two dimensions which models many physical phenomena in biological and physical sciences. The classical approach of group classification is employed for classification. We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.

Exact solubility of Chern-Simons theory with compact simple gauge group

International Nuclear Information System (INIS)

Hayashi, Masahito

1993-01-01

We show that vacuum expectation values of Wilson loop operators in (2+1)-dimensional Chern-Simons theory satisfy algebraic equations. Interestingly enough, vacuum expectation values for unknotted Wilson loop operators in any representation of any compact and simple group are exactly computed by solving the equations. So-called 'skein relations', which give us algebraic equations among vacuum expectation values of different Wilson loop operators, are constructed. In our formalism, quantum group symmetry appears naturally. (orig.)

Uniform estimate of a compact convex set by a ball in an arbitrary norm

International Nuclear Information System (INIS)

Dudov, S I; Zlatorunskaya, I V

2000-01-01

The problem of the best uniform approximation of a compact convex set by a ball with respect to an arbitrary norm in the Hausdorff metric corresponding to that norm is considered. The question is reduced to a convex programming problem, which can be studied by means of convex analysis. Necessary and sufficient conditions for the solubility of this problem are obtained and several properties of its solution are described. It is proved, in particular, that the centre of at least one ball of best approximation lies in the compact set under consideration; in addition, conditions ensuring that the centres of all balls of best approximation lie in this compact set and a condition for unique solubility are obtained

String partition functions, Hilbert schemes and affine Lie algebra representations on homology groups

International Nuclear Information System (INIS)

Bonora, Loriano; Bytsenko, Andrey; Elizalde, Emilio

2012-01-01

This review paper contains a concise introduction to highest weight representations of infinite-dimensional Lie algebras, vertex operator algebras and Hilbert schemes of points, together with their physical applications to elliptic genera of superconformal quantum mechanics and superstring models. The common link of all these concepts and of the many examples considered in this paper is to be found in a very important feature of the theory of infinite-dimensional Lie algebras: the modular properties of the characters (generating functions) of certain representations. The characters of the highest weight modules represent the holomorphic parts of the partition functions on the torus for the corresponding conformal field theories. We discuss the role of the unimodular (and modular) groups and the (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of elliptic genera and associated q-series. For mathematicians, elliptic genera are commonly associated with new mathematical invariants for spaces, while for physicists elliptic genera are one-loop string partition function. (Therefore, they are applicable, for instance, to topological Casimir effect calculations.) We show that elliptic genera can be conveniently transformed into product expressions, which can then inherit the homology properties of appropriate polygraded Lie algebras. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (review)

Reductive Lie-admissible algebras applied to H-spaces and connections

International Nuclear Information System (INIS)

Sagle, A.A.

1982-01-01

An algebra A with multiplication xy is Lie-admissible if the vector space A with new multiplication [x,y] = xy-yx is a Lie algebra; we denote this Lie algebra by A - . Thus, an associative algebra is Lie-admissible but a Cayley algebra is not Lie-admissible. In this paper we show how Lie-admissible algebras arise from Lie groups and their application to differential geometry on Lie groups via the following theorem. Let A be an n-dimensional Lie-admissible algebra over the reals. Let G be a Lie group with multiplication function μ and with Lie algebra g which is isomorphic to A - . Then there exiss a corrdinate system at the identify e in G which represents μ by a function F:gxg→g defined locally at the origin, such that the second derivative, F 2 , at the origin defines on the vector space g the structure of a nonassociative algebra (g, F 2 ). Furthermore this algebra is isomorphic to A and (g, F 2 ) - is isomorphic to A - . Thus roughly, any Lie-admissible algebra is isomorphic to an algebra obtained from a Lie algebra via a change of coordinates in the Lie group. Lie algebras arise by using canonical coordinates and the Campbell-Hausdorff formula. Applications of this show that any G-invariant psuedo-Riemannian connection on G is completely determined by a suitable Lie-admissible algebra. These results extend to H-spaces, reductive Lie-admissible algebras and connections on homogeneous H-spaces. Thus, alternative and other non-Lie-admissible algebras can be utilized

Lie-algebraic classification of effective theories with enhanced soft limits

Science.gov (United States)

Bogers, Mark P.; Brauner, Tomáš

2018-05-01

A great deal of effort has recently been invested in developing methods of calculating scattering amplitudes that bypass the traditional construction based on Lagrangians and Feynman rules. Motivated by this progress, we investigate the long-wavelength behavior of scattering amplitudes of massless scalar particles: Nambu-Goldstone (NG) bosons. The low-energy dynamics of NG bosons is governed by the underlying spontaneously broken symmetry, which likewise allows one to bypass the Lagrangian and connect the scaling of the scattering amplitudes directly to the Lie algebra of the symmetry generators. We focus on theories with enhanced soft limits, where the scattering amplitudes scale with a higher power of momentum than expected based on the mere existence of Adler's zero. Our approach is complementary to that developed recently in ref. [1], and in the first step we reproduce their result. That is, as far as Lorentz-invariant theories with a single physical NG boson are concerned, we find no other nontrivial theories featuring enhanced soft limits beyond the already well-known ones: the Galileon and the Dirac-Born-Infeld (DBI) scalar. Next, we show that in a certain sense, these theories do not admit a nontrivial generalization to non-Abelian internal symmetries. Namely, for compact internal symmetry groups, all NG bosons featuring enhanced soft limits necessarily belong to the center of the group. For noncompact symmetry groups such as the ISO( n) group featured by some multi-Galileon theories, these NG bosons then necessarily belong to an Abelian normal subgroup. The Lie-algebraic consistency constraints admit two infinite classes of solutions, generalizing the known multi-Galileon and multi-flavor DBI theories.

IEA SHC Task 42 / ECES Annex 29 - Working Group B: Applications of Compact Thermal Energy Storage

NARCIS (Netherlands)

Helden, W. van; Yamaha, M.; Rathgeber, C.; Hauer, A.; Huaylla, F.; Le Pierrès, N.; Stutz, B.; Mette, B.; Dolado, P.; Lazaro, A.; Mazo, J.; Dannemand, M.; Furbo, S.; Campos-Celador, A.; Diarce, G.; Cuypers, R.; König-Haagen, A.; Höhlein, S.; Brüggemann, D.; Fumey, B.; Weber, R.; Köll, R.; Wagner, W.; Daguenet-Frick, X.; Gantenbein, P.; Kuznik, F.

2016-01-01

The IEA joint Task 42 / Annex 29 is aimed at developing compact thermal energy storage materials and systems. In Working Group B, experts are working on the development of compact thermal energy storage applications, in the areas cooling, domestic heating and hot water and industry. The majority of

Challenges: a state and compact perspective

International Nuclear Information System (INIS)

Brown, H.

1987-01-01

The challenges facing states and compacts in their efforts to implement the Low-Level Waste Policy Amendments Act are described. Institutional challenges include: small-volume sites; compact maintenance; shifting agencies and changing personnel; and timing of progress. The technical challenge lies in the enormous number of plans, procedures, and regulations that have to be developed over the next four years. There are two main fiscal challenges: funding of day-to-day operations of compact commissions; and financing the siting and construction of new disposal sites. There are also two main regulatory challenges: host states must develop regulations for siting and selection of technology; and all states have to await federal regulations to be completed. The final challenge is political: whether a region can overcome public opposition and actually site a facility

Knot wormholes and the dimensional invariant of exceptional Lie groups and Stein space hierarchies

International Nuclear Information System (INIS)

Elokaby, Ayman

2009-01-01

The present short note points out a most interesting and quite unexpected connection between the number of distinct knot as a function of their crossing number and exceptional Lie groups and Stein space hierarchies. It is found that the crossing number 7 plays the role of threshold similar to 4 and 5 in E-infinity theory and for the 11 crossing the number of distinct knots is very close to 4α-bar 0 +1=548+1=549, where α-bar 0 =137 is the inverse integer electromagnetic fine structure constant. This is particularly intriguing in view of a similar relation pertinent to the 17 two and three Stein spaces where the total dimension is Σ 1 17 Stein=5α-bar 0 +1=685+1=686, as well as the sum of the eight exceptional Lie symmetry groups Σ i=1 8 |E i |=4α-bar 0 =548. The slight discrepancy of one is explained in both cases by the inclusion of El Naschie's transfinite corrections leading to Σ i=1 8 |E i |=(4)(137+k 0 )=548.328157 and Σ i=1 17 Stein=(5)(137+k 0 )=685.41097, where k o = φ 5 (1 - φ 5 ) and φ=(√(5)-1)/2.

Classification and identification of Lie algebras

CERN Document Server

Snobl, Libor

2014-01-01

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

Gradings on simple Lie algebras

CERN Document Server

Elduque, Alberto

2013-01-01

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

The Higgs mass derived from the U(3) Lie group

DEFF Research Database (Denmark)

Trinhammer, Ole; Bohr, Henrik; Jensen, Mogens O Stibius

2015-01-01

The Higgs mass value is derived from a Hamiltonian on the Lie group U(3) where we relate strong and electroweak energy scales. The baryon states of nucleon and delta resonances originate in specific Bloch wave degrees of freedom coupled to a Higgs mechanism which also gives rise to the usual gauge...... boson masses. The derived Higgs mass is around 125 GeV. From the same Hamiltonian, we derive the relative neutron to proton mass ratio and the N and Delta mass spectra. All compare rather well with the experimental values. We predict scarce neutral flavor baryon singlets that should be visible...... in scattering cross-sections for negative pions on protons, in photoproduction on neutrons, in neutron diffraction dissociation experiments and in invariant mass spectra of protons and negative pions in B-decays. The fundamental predictions are based on just one length scale and the fine structure constant...

A Corresponding Lie Algebra of a Reductive homogeneous Group and Its Applications

International Nuclear Information System (INIS)

Zhang Yu-Feng; Rui Wen-Juan; Wu Li-Xin

2015-01-01

With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding (2+1)-dimensional integrable hierarchy is obtained by applying the binormial-residue representation (BRR) method, whose Hamiltonian structure is derived from the trace identity for deducing (2+1)-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the (2+1)-dimensional AKNS hierarchy, the second-type reduction reveals an integrable coupling of the (2+1)-dimensional AKNS equation (also called the Davey-Stewartson hierarchy), a kind of (2+1)-dimensional Schrödinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new (2+1)-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the (2+1)-dimensional integrable coupling, which is further reduced to the standard (2+1)-dimensional diffusion equation along with a parameter. In addition, the well-known (1+1)-dimensional AKNS hierarchy, the (1+1)-dimensional nonlinear Schrödinger equation are all special cases of the (2+1)-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the von Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the (2+1)-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated. (paper)

A COMPACT GROUP OF GALAXIES AT Z = 2.48 HOSTING AN AGN-DRIVEN OUTFLOW

Energy Technology Data Exchange (ETDEWEB)

Shih, Hsin-Yi [Gemini Observatory, 670 N Aohoku Place, Hilo, HI 96720 (United States); Stockton, Alan, E-mail: jshih@gemini.edu, E-mail: stockton@ifa.hawaii.edu [Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822 (United States)

2015-12-10

We present observations of a remarkable compact group of galaxies at z = 2.48. Four galaxies, all within 40 kpc of each other, surround a powerful high-redshift radio source. This group comprises two compact red passive galaxies and a pair of merging galaxies. One of the red galaxies, with an apparent stellar mass of 3.6 × 10{sup 11}M{sub ⊙} and an effective radius of 470 pc, is one of the most extreme examples of a massive quiescent compact galaxy found so far. One of the pair of merging galaxies hosts the active galactic nucleus (AGN) producing the large powerful radio structure. The merger is massive and enriched, consistent with the mass–metallicity relation expected at this redshift. Close to the merging nuclei, the emission lines exhibit broad and asymmetric profiles that suggest outflows powered either by a very young expanding radio jet or by AGN radiation. At ≳50 kpc from the system, we found a fainter extended-emission region that may be a part of a radio-jet-driven outflow.

Testosterone administration reduces lying in men.

Directory of Open Access Journals (Sweden)

Matthias Wibral

Full Text Available 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 testosterone, which has been shown to play an important role in social behavior. In a double-blind placebo-controlled study, 91 healthy men (24.32±2.73 years received a transdermal administration of 50 mg of testosterone (n=46 or a placebo (n=45. Subsequently, subjects participated in a simple task, in which their payoff depended on the self-reported outcome of a die-roll. Subjects could increase their payoff by lying without fear of being caught. Our results show that testosterone administration substantially decreases lying in men. Self-serving lying occurred in both groups, however, reported payoffs were significantly lower in the testosterone group (p<0.01. Our results contribute to the recent debate on the effect of testosterone on prosocial behavior and its underlying channels.

Compactness of the automorphism group of a topological parallelism on real projective 3-space: The disconnected case

OpenAIRE

Rainer, Löwen

2017-01-01

We prove that the automorphism group of a topological parallelism on real projective 3-space is compact. In a preceding article it was proved that at least the connected component of the identity is compact. The present proof does not depend on that earlier result.

On a parametrization of Baker-Campbell-Hausdorf formula for bosonic superfields in Lie algebra

International Nuclear Information System (INIS)

Gabeskiria, M.A.

1984-01-01

A compact form for the Baker-Cambell-Hausdorf formula has been obtained. Here the dependence of bosonic superfields, with their values on the Crassmann hull G(LAMBDA 2 ) of Lie algebra G, on the generators LAMBDA 2 has been factorized as a single exponent

Mapping the geometry of the F4 group

International Nuclear Information System (INIS)

Bernardoni, Fabio; Cacciatori, Sergio L.; Scotti, Antonio; Cerchiai, Bianca L.

2007-01-01

In this paper, we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 Hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of F4 and its coset manifold OP2 = F4/Spin(9), the octonionic projective plane, these results are a prerequisite for the study of E6, of which F4 is a (maximal) subgroup

Applications of Lie Group Theory to the Modeling and Control of Multibody Systems

International Nuclear Information System (INIS)

Mladenova, Clementina D.

1999-01-01

This paper reviews our research activities concerning the modeling and control of rigid and elastic joint multibody mechanical systems, including some investigations into nonholonomic systems. Bearing in mind the different parameterizations of the rotation group in three-dimensional space SO(3), and the fact that the properties of the parameterization more or less influence the efficiency of the dynamics model, here the so-called vector parameter is used for parallel considerations of rigid body motion and of rigid and elastic joint multibody mechanical systems. Besides the fundamental role of this study, the vector-parameter approach is efficient in its computational aspect and quite convenient for real time simulation and control. The consideration of the mechanical system on the configuration space of pure vector parameters with a group structure opens the possibilities for the Lie group theory to be applied in problems of dynamics and control

Path integral quantization of the Symplectic Leaves of the SU(2)*Poisson-Lie Group

International Nuclear Information System (INIS)

Morariu, B.

1997-01-01

The Feynman path integral is used to quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of Uq(su(2)). This is achieved by finding explicit Darboux coordinates and then using a phase space path integral. I discuss the *-structure of SU(2)* and give a detailed description of its leaves using various parameterizations and also compare the results with the path integral quantization of spin

Bidirectional composition on lie groups for gradient-based image alignment.

Science.gov (United States)

Mégret, Rémi; Authesserre, Jean-Baptiste; Berthoumieu, Yannick

2010-09-01

In this paper, a new formulation based on bidirectional composition on Lie groups (BCL) for parametric gradient-based image alignment is presented. Contrary to the conventional approaches, the BCL method takes advantage of the gradients of both template and current image without combining them a priori. Based on this bidirectional formulation, two methods are proposed and their relationship with state-of-the-art gradient based approaches is fully discussed. The first one, i.e., the BCL method, relies on the compositional framework to provide the minimization of the compensated error with respect to an augmented parameter vector. The second one, the projected BCL (PBCL), corresponds to a close approximation of the BCL approach. A comparative study is carried out dealing with computational complexity, convergence rate and frequence of convergence. Numerical experiments using a conventional benchmark show the performance improvement especially for asymmetric levels of noise, which is also discussed from a theoretical point of view.

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

Directory of Open Access Journals (Sweden)

Kazuhiko Fukui

2017-01-01

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

Graded-Lie-algebra cohomology and supergravity

International Nuclear Information System (INIS)

D'Auria, R.; Fre, P.; Regge, T.

1980-01-01

Detailed explanations of the cohomology invoked in the group-manifold approach to supergravity is given. The Chevalley cohomology theory of Lie algebras is extended to graded Lie algebras. The scheme of geometrical theories is enlarged so to include cosmological terms and higher powers of the curvature. (author)

Koszul Information Geometry and Souriau Geometric Temperature/Capacity of Lie Group Thermodynamics

Directory of Open Access Journals (Sweden)

Frédéric Barbaresco

2014-08-01

Full Text Available 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. We will synthetize the analogies between both Koszul and Souriau models, and will reduce their definitions to the exclusive Cartan “Inner Product”. Interpreting Legendre transform as Fourier transform in (Min,+ algebra, we conclude with a definition of Entropy given by a relation mixing Fourier/Laplace transforms: Entropy = (minus Fourier(Min,+ o Log o Laplace(+,X.

Groups of integral transforms generated by Lie algebras of second-and higher-order differential operators

International Nuclear Information System (INIS)

Steinberg, S.; Wolf, K.B.

1979-01-01

The authors study the construction and action of certain Lie algebras of second- and higher-order differential operators on spaces of solutions of well-known parabolic, hyperbolic and elliptic linear differential equations. The latter include the N-dimensional quadratic quantum Hamiltonian Schroedinger equations, the one-dimensional heat and wave equations and the two-dimensional Helmholtz equation. In one approach, the usual similarity first-order differential operator algebra of the equation is embedded in the larger one, which appears as a quantum-mechanical dynamic algebra. In a second approach, the new algebra is built as the time evolution of a finite-transformation algebra on the initial conditions. In a third approach, the algebra to inhomogeneous similarity algebra is deformed to a noncompact classical one. In every case, we can integrate the algebra to a Lie group of integral transforms acting effectively on the solution space of the differential equation. (author)

Some quantum Lie algebras of type Dn positive

International Nuclear Information System (INIS)

Bautista, Cesar; Juarez-Ramirez, Maria Araceli

2003-01-01

A quantum Lie algebra is constructed within the positive part of the Drinfeld-Jimbo quantum group of type D 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 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

Conjugation weights and weighted convolution algebras on totally disconnected, locally compact groups

OpenAIRE

Willis, George

2013-01-01

A family of equivalent submultiplicative weights on the to- tally disconnected, locally compact group $G$ is defined in terms of the conjugation action of $G$ on itself. These weights therefore reflect the structure of $G$, and the corresponding weighted convolution algebra is intrinsic to $G$ in the same way that $L^1(G) is.

Lie Quasi-Bialgebras and Cohomology of Lie algebra

International Nuclear Information System (INIS)

Bangoura, Momo

2010-05-01

Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, μ, γ, φ), corresponds one Lie algebra structure on D = G + G*, called the double of the given Lie quasi-bialgebra. We show that there exist on ΛG, the exterior algebra of G, a D-module structure and we establish an isomorphism of D-modules between ΛD and End(ΛG), D acting on ΛD by the adjoint action. (author) [fr

Lie group model neuromorphic geometric engine for real-time terrain reconstruction from stereoscopic aerial photos

Science.gov (United States)

Tsao, Thomas R.; Tsao, Doris

1997-04-01

In the 1980's, neurobiologist suggested a simple mechanism in primate visual cortex for maintaining a stable and invariant representation of a moving object. The receptive field of visual neurons has real-time transforms in response to motion, to maintain a stable representation. When the visual stimulus is changed due to motion, the geometric transform of the stimulus triggers a dual transform of the receptive field. This dual transform in the receptive fields compensates geometric variation in the stimulus. This process can be modelled using a Lie group method. The massive array of affine parameter sensing circuits will function as a smart sensor tightly coupled to the passive imaging sensor (retina). Neural geometric engine is a neuromorphic computing device simulating our Lie group model of spatial perception of primate's primal visual cortex. We have developed the computer simulation and experimented on realistic and synthetic image data, and performed a preliminary research of using analog VLSI technology for implementation of the neural geometric engine. We have benchmark tested on DMA's terrain data with their result and have built an analog integrated circuit to verify the computational structure of the engine. When fully implemented on ANALOG VLSI chip, we will be able to accurately reconstruct a 3D terrain surface in real-time from stereoscopic imagery.

Compatible Lie Bialgebras

International Nuclear Information System (INIS)

Wu Ming-Zhong; Bai Cheng-Ming

2015-01-01

A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie algebras as an analogue of a Lie bialgebra. They can also be regarded as a “compatible version” of Lie bialgebras, that is, a pair of Lie bialgebras such that any linear combination of the two Lie bialgebras is still a Lie bialgebra. Many properties of compatible Lie bialgebras as the “compatible version” of the corresponding properties of Lie bialgebras are presented. In particular, there is a coboundary compatible Lie bialgebra theory with a construction from the classical Yang–Baxter equation in compatible Lie algebras as a combination of two classical Yang–Baxter equations in Lie algebras. Furthermore, a notion of compatible pre-Lie algebra is introduced with an interpretation of its close relation with the classical Yang–Baxter equation in compatible Lie algebras which leads to a construction of the solutions of the latter. As a byproduct, the compatible Lie bialgebras fit into the framework to construct non-constant solutions of the classical Yang–Baxter equation given by Golubchik and Sokolov. (paper)

Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group with motivations from string theory and QFT

Directory of Open Access Journals (Sweden)

Khodakhast Bibak

2016-09-01

Full Text Available Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT. Recently, Koch et al. (2013 [12] gave a refined formula for counting ribbon graphs and discussed its applications to several physics problems. An important factor in this formula is the number of surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group. The aim of this paper is to give an explicit and practical formula for the number of such epimorphisms. As a consequence, we obtain an ‘equivalent’ form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.

Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group with motivations from string theory and QFT

Energy Technology Data Exchange (ETDEWEB)

Bibak, Khodakhast, E-mail: kbibak@uvic.ca; Kapron, Bruce M., E-mail: bmkapron@uvic.ca; Srinivasan, Venkatesh, E-mail: srinivas@uvic.ca

2016-09-15

Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT). Recently, Koch et al. (2013) gave a refined formula for counting ribbon graphs and discussed its applications to several physics problems. An important factor in this formula is the number of surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group. The aim of this paper is to give an explicit and practical formula for the number of such epimorphisms. As a consequence, we obtain an ‘equivalent’ form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.

On the q-exponential of matrix q-Lie algebras

Directory of Open Access Journals (Sweden)

Ernst Thomas

2017-01-01

Full Text Available In this paper, we define several new concepts in the borderline between linear algebra, Lie groups and q-calculus.We first introduce the ring epimorphism r, the set of all inversions of the basis q, and then the important q-determinant and corresponding q-scalar products from an earlier paper. Then we discuss matrix q-Lie algebras with a modified q-addition, and compute the matrix q-exponential to form the corresponding n × n matrix, a so-called q-Lie group, or manifold, usually with q-determinant 1. The corresponding matrix multiplication is twisted under τ, which makes it possible to draw diagrams similar to Lie group theory for the q-exponential, or the so-called q-morphism. There is no definition of letter multiplication in a general alphabet, but in this article we introduce new q-number systems, the biring of q-integers, and the extended q-rational numbers. Furthermore, we provide examples of matrices in suq(4, and its corresponding q-Lie group. We conclude with an example of system of equations with Ward number coeficients.

Quasi exceptional E12 Lie symmetry group with 685 dimensions, KAC-Moody algebra and E-infinity Cantorian spacetime

International Nuclear Information System (INIS)

El Naschie, M.S.

2008-01-01

The short note gives a derivation for a new E12 exceptional Lie group corresponding to affine KAC-Moody algebra. We derive the dimension of the group by intersectionally embedding the intrinsic dimension of E8 namely D(E8) = 57 into the 12 spacetime dimensions of F theory and finding that Dim E12 = D(E8) (DF) + 1 = (57)(12) + 1 = 685

Steady nanofluid flow with variable fluid possessions over a linearly extending surface: A Lie group exploration

Directory of Open Access Journals (Sweden)

Kalidas Das

2018-03-01

Full Text Available The temperament of stream characteristic, heat and mass transfer of MHD forced convective flow over a linearly expanding porous medium has been scrutinized in the progress exploration. The germane possessions of the liquid like viscosity along with thermal conductivity are believed to be variable in nature, directly influenced by the temperature of flow. As soon as gaining the system of leading equations of the stream, Lie symmetric group transformations have been employed to come across the fitting parallel conversions to alter the central PDEs into a suit of ODEs. The renovated system of ODE with appropriate boundary conditions is numerically solved with the assistance of illustrative software MAPLE 17. The consequences of the relevant factors of the system have been exemplified through charts and graphs. An analogous qualified survey has been prepared among present inquiry and subsisting reads and achieved an admirable accord between them. The variable viscosity parameter has more significant effect on nanofluid velocity than regular fluid and temporal profile as well as nanoparticle concentration is also influenced with variable viscosity. Keywords: Nanofluid, Stretching sheet, Variable viscosity, Variable thermal conductivity, Lie symmetry group

6th Hilbert's problem and S.Lie's infinite groups

International Nuclear Information System (INIS)

Konopleva, N.P.

1999-01-01

The progress in Hilbert's sixth problem solving is demonstrated. That became possible thanks to the gauge field theory in physics and to the geometrical treatment of the gauge fields. It is shown that the fibre bundle spaces geometry is the best basis for solution of the problem being discussed. This talk has been reported at the International Seminar '100 Years after Sophus Lie' (Leipzig, Germany)

Lying to patients with dementia: Attitudes versus behaviours in nurses.

Science.gov (United States)

Cantone, Daniela; Attena, Francesco; Cerrone, Sabrina; Fabozzi, Antonio; Rossiello, Riccardo; Spagnoli, Laura; Pelullo, Concetta Paola

2017-01-01

Using lies, in dementia care, reveals a common practice far beyond the diagnosis and prognosis, extending to the entire care process. In this article, we report results about the attitude and the behaviour of nurses towards the use of lies to patients with dementia. An epidemiological cross-sectional study was conducted between September 2016 and February 2017 in 12 elderly residential facilities and in the geriatric, psychiatric and neurological wards of six specialised hospitals of Italy's Campania Region. In all, 106 nurses compiled an attitude questionnaire (A) where the main question was 'Do you think it is ethically acceptable to use lies to patients with dementia?', instead 106 nurses compiled a behaviour questionnaire (B), where the main question was 'Have you ever used lies to patients with dementia?' Ethical considerations: Using lies in dementia care, although topic ethically still controversial, reveals a common practice far beyond the diagnosis and prognosis, extending to the entire care process. Only a small percentage of the interviewed nurses stated that they never used lies/that it is never acceptable to use lies (behaviour 10.4% and attitude 12.3%; p = 0.66). The situation in which nurses were more oriented to use lies was 'to prevent or reduce aggressive behaviors'. Indeed, only the 6.7% in the attitude group and 3.8% in the behaviour group were against using lies. On the contrary, the case in which the nurses were less oriented to use lies was 'to avoid wasting time giving explanations', in this situation were against using lies the 51.0% of the behaviour group and the 44.6% of the attitude group. Our results, according to other studies, support the hypothesis of a low propensity of nurses to ethical reflection about use of lies. In our country, the implementation of guidelines about a correct use of lie in the relationship between health operators and patients would be desirable.

Lagrangian submanifolds and dynamics on Lie algebroids

International Nuclear Information System (INIS)

Leon, Manuel de; Marrero, Juan C; MartInez, Eduardo

2005-01-01

In some previous papers, a geometric description of Lagrangian mechanics on Lie algebroids has been developed. In this topical review, we give a Hamiltonian description of mechanics on Lie algebroids. In addition, we introduce the notion of a Lagrangian submanifold of a symplectic Lie algebroid and we prove that the Lagrangian (Hamiltonian) dynamics on Lie algebroids may be described in terms of Lagrangian submanifolds of symplectic Lie algebroids. The Lagrangian (Hamiltonian) formalism on Lie algebroids permits us to deal with Lagrangian (Hamiltonian) functions not defined necessarily on tangent (cotangent) bundles. Thus, we may apply our results to the projection of Lagrangian (Hamiltonian) functions which are invariant under the action of a symmetry Lie group. As a consequence, we obtain that Lagrange-Poincare (Hamilton-Poincare) equations are the Euler-Lagrange (Hamilton) equations associated with the corresponding Atiyah algebroid. Moreover, we prove that Lagrange-Poincare (Hamilton-Poincare) equations are the local equations defining certain Lagrangian submanifolds of symplectic Atiyah algebroids. (topical review)

't Hooft's solution for arbitrary semisimple Lie group

International Nuclear Information System (INIS)

Leznov, A.N.; Mukhtarov, M.A.

1990-07-01

The generalization of the 't Hooft's A 1 solution for every semisimple Lie algebra is found. The solution depends on r-independent chains of linear self-dual systems (Δ s α ) z = (Δ s+1 α ) y -bar, (Δ s α ) y -bar = -(Δ s+1 α ) z (1 ≤ α ≤ r); the length of α chain is equal to 2ω α + 1, where ω α are the indexes of the semisimple algebra and r is its rank. In the special case the O(4)-invariant solutions with instanton number equal to one arises. (author). 6 refs

Start-up scenario of compact tori based on REB-injection developed in SPAC-group

International Nuclear Information System (INIS)

Ikuta, K.

1981-01-01

Quasi-static start-up of compact tori without toroidal field coil is reviewed thoroughly in a proposal of the S-1 spheromak. During the formation phase we should note that the rapid heat loss from the plasma will give a bad effect for the generation of the confinement configuration. In the case of fast start-up of the configuration plasma can safely pass over the dangerous state of the instability toward the desirable stable state with a bonus of producing hot plasma. By this reason it is intended to discuss a fast start-up scenario of the compact tori based on REB injection developed in SPAC group

Hierarchy of kissing numbers for exceptional Lie symmetry groups in high energy physics

International Nuclear Information System (INIS)

El Naschie, M.S.

2008-01-01

We are constructing a hierarchy of kissing numbers representing singular contact points of hyper-spheres in exceptional Lie symmetry groups lattice arrangement embedded in the 26 dimensional bosonic strings spacetime. That way we find a total number of points and dimensions equal to 548. This is 52 more than the order of E 8 E 8 of heterotic string theory and leads to the prediction of 69 elementary particles at an energy scale under 1 T. In other words, our mathematical model predicts nine more particles than what is currently experimentally known to exist in the standard model of high energy physics namely only 60. The result is thus in full agreement with all our previous theoretical findings

Realization of vector fields for quantum groups as pseudodifferential operators on quantum spaces

International Nuclear Information System (INIS)

Chu, Chong-Sun; Zumino, B.

1995-01-01

The vector fields of the quantum Lie algebra are described for the quantum groups GL q (n), SL q (N) and SO q (N) as pseudodifferential operators on the linear quantum spaces covariant under the corresponding quantum group. Their expressions are simple and compact. It is pointed out that these vector fields satisfy certain characteristic polynomial identities. The real forms SU q (N) and SO q (N,R) are discussed in detail

Particle-like structure of coaxial Lie algebras

Science.gov (United States)

Vinogradov, A. M.

2018-01-01

This paper is a natural continuation of Vinogradov [J. Math. Phys. 58, 071703 (2017)] where we proved that any Lie algebra over an algebraically closed field or over R can be assembled in a number of steps from two elementary constituents, called dyons and triadons. Here we consider the problems of the construction and classification of those Lie algebras which can be assembled in one step from base dyons and triadons, called coaxial Lie algebras. The base dyons and triadons are Lie algebra structures that have only one non-trivial structure constant in a given basis, while coaxial Lie algebras are linear combinations of pairwise compatible base dyons and triadons. We describe the maximal families of pairwise compatible base dyons and triadons called clusters, and, as a consequence, we give a complete description of the coaxial Lie algebras. The remarkable fact is that dyons and triadons in clusters are self-organised in structural groups which are surrounded by casings and linked by connectives. We discuss generalisations and applications to the theory of deformations of Lie algebras.

On the definition of an admitted Lie group for stochastic differential equations with multi-Brownian motion

International Nuclear Information System (INIS)

Srihirun, B; Meleshko, S V; Schulz, E

2006-01-01

The definition of an admitted Lie group of transformations for stochastic differential equations has been already presented for equations with one-dimensional Brownian motion. The transformation of the dependent variables involves time as well, and it has been proven that Brownian motion is transformed to Brownian motion. In this paper, we will discuss this concept for stochastic differential equations involving multi-dimensional Brownian motion and present applications to a variety of stochastic differential equations

GALAXY INTERACTIONS IN COMPACT GROUPS. I. THE GALACTIC WINDS OF HCG16

Energy Technology Data Exchange (ETDEWEB)

Vogt, Frederic P. A.; Dopita, Michael A.; Kewley, Lisa J., E-mail: fvogt@mso.anu.edu.au [Mount Stromlo Observatory, Research School of Astronomy and Astrophysics, Australian National University, Cotter Road, Weston Creek, ACT 2611 (Australia)

2013-05-10

Using the WiFeS integral field spectrograph, we have undertaken a series of observations of star-forming galaxies in compact groups. In this first paper dedicated to the project, we present the analysis of the spiral galaxy NGC 838, a member of the Hickson Compact Group 16, and of its galactic wind. Our observations reveal that the wind forms an asymmetric, bipolar, rotating structure, powered by a nuclear starburst. Emission line ratio diagnostics indicate that photoionization is the dominant excitation mechanism at the base of the wind. Mixing from slow shocks (up to 20%) increases further out along the outflow axis. The asymmetry of the wind is most likely caused by one of the two lobes of the wind bubble bursting out of its H I envelope, as indicated by line ratios and radial velocity maps. The characteristics of this galactic wind suggest that it is caught early (a few Myr) in the wind evolution sequence. The wind is also quite different from the galactic wind in the partner galaxy NGC 839 which contains a symmetric, shock-excited wind. Assuming that both galaxies have similar interaction histories, the two different winds must be a consequence of the intrinsic properties of NGC 838 and NGC 839 and their starbursts.

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

International Nuclear Information System (INIS)

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

1990-01-01

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

Lie-superalgebraical aspects of quantum statistics

International Nuclear Information System (INIS)

Palev, T.D.

1978-01-01

The Lie-superalgebraical properties of the ordinary quantum statistics are discussed with the aim of possible generalization in quantum theory and in theoretical physics. It is indicated that the algebra generated by n pairs of Fermi or paraFermi operators is isomorphic to the classical simple Lie algebra Bsub(n) of the SO(2n+1) orthogonal group, whereas n pairs of Bose or paraBose operators generate the simple orthosympletic superalgebra B(O,n). The transition to infinite number of creation and annihilation operators (n → infinity) does not change a superalgebraic structure. Hence, ordinary Bose and Fermi quantization can be considered as quantization over definite irreducible representations of two simple Lie superalgebras. The idea is given of how one can introduce creation and annihilation operators that satisfy the second quantization postulates and generate other simple Lie superalgebras

Grupos de Lie

OpenAIRE

Rubio Martí, Vicente

2016-01-01

En el presente proyecto definimos lo que es un grupo de Lie, así como su respectiva álgebra de Lie canónica como aproximación lineal a dicho grupo de Lie. El proceso de linealización, que es hallar el algebra de Lie de un grupo de Lie dado, tiene su

Mappings with closed range and compactness

International Nuclear Information System (INIS)

Iyahen, S.O.; Umweni, I.

1985-12-01

The motivation for this note is the result of E.O. Thorp that a normed linear space E is finite dimensional if and only if every continuous linear map for E into any normed linear space has a closed range. Here, a class of Hausdorff topological groups is introduced; called r-compactifiable topological groups, they include compact groups, locally compact Abelian groups and locally convex linear topological spaces. It is proved that a group in this class which is separable, complete metrizable or locally compact, is necessarily compact if its image by a continuous group homomorphism is necessarily closed. It is deduced then that a Hausdorff locally convex is zero if its image by a continuous additive map is necessarily closed. (author)

Testing the Binary Black Hole Nature of a Compact Binary Coalescence.

Science.gov (United States)

Krishnendu, N V; Arun, K G; Mishra, Chandra Kant

2017-09-01

We propose a novel method to test the binary black hole nature of compact binaries detectable by gravitational wave (GW) interferometers and, hence, constrain the parameter space of other exotic compact objects. The spirit of the test lies in the "no-hair" conjecture for black holes where all properties of a Kerr black hole are characterized by its mass and spin. The method relies on observationally measuring the quadrupole moments of the compact binary constituents induced due to their spins. If the compact object is a Kerr black hole (BH), its quadrupole moment is expressible solely in terms of its mass and spin. Otherwise, the quadrupole moment can depend on additional parameters (such as the equation of state of the object). The higher order spin effects in phase and amplitude of a gravitational waveform, which explicitly contains the spin-induced quadrupole moments of compact objects, hence, uniquely encode the nature of the compact binary. Thus, we argue that an independent measurement of the spin-induced quadrupole moment of the compact binaries from GW observations can provide a unique way to distinguish binary BH systems from binaries consisting of exotic compact objects.

Compact stars in f(R, T) gravity

Energy Technology Data Exchange (ETDEWEB)

Das, Amit; Guha, B.K. [Indian Institute of Engineering Science and Technology, Department of Physics, Howrah, West Bengal (India); Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India)

2016-12-15

In the present paper we generate a set of solutions describing the interior of a compact star under f(R, T) theory of gravity which admits conformal motion. An extension of general relativity, the f(R, T) gravity is associated to Ricci scalar R and the trace of the energy-momentum tensor T. To handle the Einstein field equations in the form of differential equations of second order, first of all we adopt the Lie algebra with conformal Killing vectors (CKV) which enable one to get a solvable form of such equations and second we consider the equation of state (EOS) p = ωρ with 0 < ω < 1 for the fluid distribution consisting of normal matter, ω being the EOS parameter. We therefore analytically explore several physical aspects of the model to represent behavior of the compact stars such as - energy conditions, TOV equation, stability of the system, Buchdahl condition, compactness and redshift. It is checked that the physical validity and the acceptability of the present model within the specified observational constraint in connection to a dozen of the compact star candidates are quite satisfactory. (orig.)

Classification of stationary compact homogeneous special pseudo K\\"ahler manifolds of semisimple groups

OpenAIRE

Alekseevsky, D. V.; Cortes, V.

1997-01-01

The variation of Hodge structure of a Calabi-Yau 3-fold induces a canonical K\\"ahler metric on its Kuranishi moduli space, known as the Weil-Petersson metric. Similarly, special pseudo K\\"ahler manifolds correspond to certain (abstract) variations of Hodge structure which generalize the above example. We give the classification of homogeneous special pseudo K\\"ahler manifolds of semisimple groups with compact stabilizer.

Transitive Lie algebras of vector fields: an overview

NARCIS (Netherlands)

Draisma, J.

2011-01-01

This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary differential equations, these algebras, or infinitesimal groups, are a recurring theme in 20th-century research on

Unitary Representations of Gauge Groups

Science.gov (United States)

Huerfano, Ruth Stella

I generalize to the case of gauge groups over non-trivial principal bundles representations that I. M. Gelfand, M. I. Graev and A. M. Versik constructed for current groups. The gauge group of the principal G-bundle P over M, (G a Lie group with an euclidean structure, M a compact, connected and oriented manifold), as the smooth sections of the associated group bundle is presented and studied in chapter I. Chapter II describes the symmetric algebra associated to a Hilbert space, its Hilbert structure, a convenient exponential and a total set that later play a key role in the construction of the representation. Chapter III is concerned with the calculus needed to make the space of Lie algebra valued 1-forms a Gaussian L^2-space. This is accomplished by studying general projective systems of finitely measurable spaces and the corresponding systems of sigma -additive measures, all of these leading to the description of a promeasure, a concept modeled after Bourbaki and classical measure theory. In the case of a locally convex vector space E, the corresponding Fourier transform, family of characters and the existence of a promeasure for every quadratic form on E^' are established, so the Gaussian L^2-space associated to a real Hilbert space is constructed. Chapter III finishes by exhibiting the explicit Hilbert space isomorphism between the Gaussian L ^2-space associated to a real Hilbert space and the complexification of its symmetric algebra. In chapter IV taking as a Hilbert space H the L^2-space of the Lie algebra valued 1-forms on P, the gauge group acts on the motion group of H defining in an straight forward fashion the representation desired.

Some quantum Lie algebras of type D{sub n} positive

Energy Technology Data Exchange (ETDEWEB)

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.

Compaction of spent nuclear fuel cans

International Nuclear Information System (INIS)

Sullivan, H.

1985-01-01

Hydraulic press apparatus for compacting waste material eg. spent nuclear fuel cans comprises a fixed frame, a movable cross head, a press crown and three groups of piston/cylinder devices; having their pistons connected to the cross head and their cylinders secured to the press crown. A control means connects the first group of devices to hydraulic fluid in a reservoir which is pressurised initially by gas from gas accumulators to move the cross head and a quill secured thereto towards the frame base to compact the waste at a first high rate under a first high loading. Compaction then proceeds at a lower second rate at a lower second loading as the hydraulic fluid in the reservoir is pressurised by a pump. At two subsequent stages of compaction of the waste at which resistance increases causing a pressure rise in cylinders the control means causes hydraulic fluid to be passed to the second group of devices and thence to the third group of devices, the compaction rate reducing at each stage but the compaction force increasing. (author)

On the torus cobordant cohomology spheres

Indian Academy of Sciences (India)

Let a compact Lie group G act on a smooth integral cohomology sphere with G = .... is a compact connected Lie group, (X, A) is a G space and H. ∗ ..... [15] Hsiang W-Y, Cohomology theory of topological transformation groups (New York,.

Lie symmetries in differential equations

International Nuclear Information System (INIS)

Pleitez, V.

1979-01-01

A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt

Transverse lie in labor: A study from Kaduna, Northern Nigeria ...

African Journals Online (AJOL)

Results: During the period there were 16633 deliveries and 30 women with transversely lying fetuses, giving an incidence of 1 in 554 deliveries. Forty percent of the cases were neglected transverse lies. The para 4 and above group had the highest incidence of 2.69/1000. Northern minorities ethnic group had the highest ...

Sophus Lie une pensée audacieuse

CERN Document Server

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

"Lie to me"-Oxytocin impairs lie detection between sexes.

Science.gov (United States)

Pfundmair, Michaela; Erk, Wiebke; Reinelt, Annika

2017-10-01

The hormone oxytocin modulates various aspects of social behaviors and even seems to lead to a tendency for gullibility. The aim of the current study was to investigate the effect of oxytocin on lie detection. We hypothesized that people under oxytocin would be particularly susceptible to lies told by people of the opposite sex. After administration of oxytocin or a placebo, male and female participants were asked to judge the veracity of statements from same- vs. other-sex actors who either lied or told the truth. Results showed that oxytocin decreased the ability of both male and female participants to correctly classify other-sex statements as truths or lies compared to placebo. This effect was based on a lower ability to detect lies and not a stronger bias to regard truth statements as false. Revealing a new effect of oxytocin, the findings may support assumptions about the hormone working as a catalyst for social adaption. Copyright © 2017. Published by Elsevier Ltd.

Progreso técnico: una aproximación desde la Teoría de Grupos de Transformaciones de Lie || Technical progress: an aproach from Lie Transformation Group Theory

Directory of Open Access Journals (Sweden)

Fedriani Martel, Eugenio M.

2006-06-01

Full Text Available En la presente comunicación explicamos algunas de las herramientas de la Geometría Diferencial y, en concreto, de la Teoría de Lie con las que se trabaja actualmente en Economía. Se indican las condiciones que se exigen a las funciones de producción y la definición de un tipo de progreso técnico denominado de tipo Lie, consistente en exigir las tres propiedades que han de verificar los grupos de Lie. También se expone el uso del operador de Lie en interpretaciones económicas y en la cuantificación del impacto del progreso técnico. Dicho operador permite dar una respuesta a la Controversia Solow-Stigler. Por último, se indican varias aplicaciones de la Teoría de Lie en los estudios económicos, que permiten abrir futuras líneas de investigación,de las que se apuntan algunas. De este modo, nuestro objetivo principal es mostrar el uso, actual y futuro, de la Teoría de Lie en el campo de la Economía.

Bond behavior of self compacting concrete

Directory of Open Access Journals (Sweden)

Ponmalar S.

2018-03-01

Full Text Available The success of an optimum design lies in the effective load transfer done by the bond forces at the steel-concrete interface. Self Compacting Concrete, is a new innovative concrete capable of filling intrinsic reinforcement and gets compacted by itself, without the need of external mechanical vibration. For this reason, it is replacing the conventional vibrated concrete in the construction industry. The present paper outlays the materials and methods adopted for attaining the self compacting concrete and describes about the bond behavior of this concrete. The bond stress-slip curve is similar in the bottom bars for both SCC and normal concrete whereas a higher bond stress and stiffness is experienced in the top and middle bars, for SCC compared to normal concrete. Also the interfacial properties revealed that the elastic modulus and micro-strength of interfacial transition zone [ITZ] were better on the both top and bottom side of horizontal steel bar in the SCC mixes than in normal vibrated concrete. The local bond strength of top bars for SCC is about 20% less than that for NC. For the bottom bars, however, the results were almost the same.

Bond behavior of self compacting concrete

Science.gov (United States)

Ponmalar, S.

2018-03-01

The success of an optimum design lies in the effective load transfer done by the bond forces at the steel-concrete interface. Self Compacting Concrete, is a new innovative concrete capable of filling intrinsic reinforcement and gets compacted by itself, without the need of external mechanical vibration. For this reason, it is replacing the conventional vibrated concrete in the construction industry. The present paper outlays the materials and methods adopted for attaining the self compacting concrete and describes about the bond behavior of this concrete. The bond stress-slip curve is similar in the bottom bars for both SCC and normal concrete whereas a higher bond stress and stiffness is experienced in the top and middle bars, for SCC compared to normal concrete. Also the interfacial properties revealed that the elastic modulus and micro-strength of interfacial transition zone [ITZ] were better on the both top and bottom side of horizontal steel bar in the SCC mixes than in normal vibrated concrete. The local bond strength of top bars for SCC is about 20% less than that for NC. For the bottom bars, however, the results were almost the same.

Discrete finite nilpotent Lie analogs: New models for unified gauge field theory

International Nuclear Information System (INIS)

Kornacker, K.

1978-01-01

To each finite dimensional real Lie algebra with integer structure constants there corresponds a countable family of discrete finite nilpotent Lie analogs. Each finite Lie analog maps exponentially onto a finite unipotent group G, and is isomorphic to the Lie algebra of G. Reformulation of quantum field theory in discrete finite form, utilizing nilpotent Lie analogs, should elminate all divergence problems even though some non-Abelian gauge symmetry may not be spontaneously broken. Preliminary results in the new finite representation theory indicate that a natural hierarchy of spontaneously broken symmetries can arise from a single unbroken non-Abelian gauge symmetry, and suggest the possibility of a new unified group theoretic interpretation for hadron colors and flavors

Lie Superalgebras

CERN Document Server

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.

Gruppi, anelli di Lie e teoria della coomologia

CERN Document Server

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.

Wess-Zumino-Novikov-Witten models based on Lie superalgebras

International Nuclear Information System (INIS)

Mohammedi, N.

1994-04-01

The affine current algebra for Lie superalgebras is examined. The bilinear invariant forms of the Lie superalgebra can be either degenerate or non-degenerate. We give the conditions for a Virasoro construction, in which the currents are primary fields of weight one, to exist. In certain cases, the Virasoro central charge is an integer equal to the super dimension of the group supermanifold. A Wess-Zumino-Novikov-Witten action based on these Lie superalgebras is also found. (orig.)

Conditionally exponential convex functions on locally compact groups

International Nuclear Information System (INIS)

Okb El-Bab, A.S.

1992-09-01

The main results of the thesis are: 1) The construction of a compact base for the convex cone of all conditionally exponential convex functions. 2) The determination of the extreme parts of this cone. Some supplementary lemmas are proved for this purpose. (author). 8 refs

Deformations of classical Lie algebras with homogeneous root system in characteristic two. I

International Nuclear Information System (INIS)

Chebochko, N G

2005-01-01

Spaces of local deformations of classical Lie algebras with a homogeneous root system over a field K of characteristic 2 are studied. By a classical Lie algebra over a field K we mean the Lie algebra of a simple algebraic Lie group or its quotient algebra by the centre. The description of deformations of Lie algebras is interesting in connection with the classification of the simple Lie algebras.

Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics

International Nuclear Information System (INIS)

Czachor, M.

1996-01-01

Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)

Multiplication: From Thales to Lie1

Indian Academy of Sciences (India)

Addition. To describe the geometric constructions of addition, as ..... general, we could apply the implicit function theorem of calculus to solve locally the defining ... and whose multiplication and inverse are analytic maps, is called a Lie group.

Symmetries and groups in particle physics

International Nuclear Information System (INIS)

Scherer, Stefan

2016-01-01

The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to

Dimensional reduction of exceptional E6,E8 gauge groups and flavour chirality

International Nuclear Information System (INIS)

Koca, M.

1984-01-01

Ten-dimensional Yang - Mills gauge theories based on the exceptional groups E 6 and E 8 are reduced to four-dimensional flavour-chiral Yang - Mills - Higgs theories where the extra six dimensions are identified with the compact G 2 /SU(3) and SO(7)/SO(6) coset spaces. A ten-dimensional E 8 theory leads to three families of SU(5), one of which lies in the 144-dimensional representation of SO(10)

Lying in the Name of the Collective Good: A Developmental Study

Science.gov (United States)

Fu, Genyue; Evans, Angela D.; Wang, Lingfeng; Lee, Kang

2008-01-01

The present study examined the developmental origin of "blue lies", a pervasive form of lying in the adult world that is told purportedly to benefit a collective. Seven, 9-, and 11-year-old Chinese children were surreptitiously placed in a real-life situation where they decided whether to lie to conceal their group's cheating behavior. Children…

On the use of the Lie group technique for differential equations with a small parameter: Approximate solutions and integrable equations

International Nuclear Information System (INIS)

Burde, G.I.

2002-01-01

A new approach to the use of the Lie group technique for partial and ordinary differential equations dependent on a small parameter is developed. In addition to determining approximate solutions to the perturbed equation, the approach allows constructing integrable equations that have solutions with (partially) prescribed features. Examples of application of the approach to partial differential equations are given

Abstract structure of partial function $*$-algebras over semi-direct product of locally compact groups

Directory of Open Access Journals (Sweden)

Arash Ghaani Farashahi

2015-12-01

Full Text Available This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-convolution on $L^1(G_tau$ and we show that, with respect to each of them, the function space $L^1(G_tau$ is a Banach algebra. We define $tau$-convolution as a linear combination of the left and right $tau$-convolution and we show that the $tau$-convolution is commutative if and only if $K$ is abelian. We prove that there is a $tau$-involution on $L^1(G_tau$ such that with respect to the $tau$-involution and $tau$-convolution, $L^1(G_tau$ is a non-associative Banach $*$-algebra. It is also shown that when $K$ is abelian, the $tau$-involution and $tau$-convolution make $L^1(G_tau$ into a Jordan Banach $*$-algebra. Finally, we also present the generalized notation of $tau$-convolution for other $L^p$-spaces with $p>1$.

Gabor frames on locally compact abelian groups and related topics

DEFF Research Database (Denmark)

Jakobsen, Mads Sielemann

This thesis consists of four papers. The first one introduces generalized translation invariant systems and considers their frame properties, the second and third paper give new results on the theory of Gabor frames, and the fourth is a review paper with proofs and new results on the Feichtinger......- and shearlet-type and for (generalized) shift-invariant systems and their continuous formulations. This thesis advances the theory of both separable and non-separable, discrete, semicontinuous and continuous Gabor systems. In particular, the well established structure theory for separable lattice Gabor frames...... and Gabor Riesz bases. The theory of GTI systems and Gabor frames in this thesis is developed and presented in the setting of locally compact abelian groups, however, even in the euclidean setting the results given here improve the existing theory. Finally, the thesis contains a review paper with proofs...

Ultra-compact high velocity clouds in the ALFALFA HI survey: Candidate Local Group galaxies?

Science.gov (United States)

Adams, Elizabeth Ann Kovenz

The increased sensitivity and spatial resolution of the ALFALFA HI survey has resulted in the detection of ultra-compact high velocity clouds (UCHVCs). These objects are good candidates to represent low mass gas-rich galaxies in the Local Group and Local Volume with stellar populations that are too faint to be detected in extant optical surveys. This idea is referred to as the "minihalo hypothesis". We identify the UCHVCs within the ALFALFA dataset via the use of a 3D matched filtering signal identification algorithm. UCHVCs are selected based on a compact size ( 120 km s-1) and isolation. Within the 40% complete ALFALFA survey (alpha.40), 59 UCHVCs are identified; 19 are in a most-isolated subset and are the best galaxy candidates. Due to the presence of large HVC complexes in the fall sky, most notably the Magellanic Stream, the association of UCHVCs with existing structure cannot be ruled out. In the spring sky, the spatial and kinematic distribution of the UCHVCs is consistent with simulations of dark matter halos within the Local Group. In addition, the HI properties of the UCHVCs (if placed at 1 Mpc) are consistent with both theoretical and observational predictions for low mass gas-rich galaxies. Importantly, the HI properties of the UCHVCs are consistent with those of two recently discovered low mass gas-rich galaxies in the Local Group and Local Volume, Leo T and Leo P. Detailed follow-up observations are key for addressing the minihalo hypothesis. High resolution HI observations can constrain the environment of a UCHVC and offer evidence for a hosting dark matter halo through evidence of rotation support and comparison to theoretical models. Observations of one UCHVC at high resolution (15'') reveal the presence of a clumpy HI distribution, similar to both low mass galaxies and circumgalactic compact HVCs. An extended envelope containing ˜50% of the HI flux is resolved out by the array configuration; observations at lower spatial resolution can recover

Moduli space of self-dual connections in dimension greater than four for abelian Gauge groups

OpenAIRE

Cappelle, Natacha

2018-01-01

In 1954, C. Yang and R. Mills created a Gauge Theory for strong interaction of Elementary Particles. More generally, they proved that it is possible to define a Gauge Theory with an arbitrary compact Lie group as Gauge group. Within this context, it is interesting to find critical values of a functional defined on the space of connections: the Yang-Mills functional. If the based manifold is four dimensional, there exists a natural notion of (anti-)self-dual 2-form, which gives a natural notio...

Quantum isometry groups

Indian Academy of Sciences (India)

Jyotishman Bhowmick

2015-11-07

Nov 7, 2015 ... Classical. Quantum. Background. Compact Hausdorff space. Unital C∗ algebra. Gelfand-Naimark. Compact Group. Compact Quantum Group. Woronowicz. Group Action. Coaction. Woronowicz. Riemannian manifold. Spectral triple. Connes. Isometry group. Quantum Isometry Group. To be discussed.

Sugawara operators for classical Lie algebras

CERN Document Server

Molev, Alexander

2018-01-01

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

Counting Semisimple Orbits of Finite Lie Algebras by Genus

OpenAIRE

Fulman, Jason

1999-01-01

The adjoint action of a finite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are obtained for other types. For type A a probabilistic interpretation is given in terms of card shuffling.

Bases in Lie and quantum algebras

International Nuclear Information System (INIS)

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

2008-01-01

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

Flux formulation of DFT on group manifolds and generalized Scherk-Schwarz compactifications

Energy Technology Data Exchange (ETDEWEB)

Bosque, Pascal du [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Arnold-Sommerfeld-Center für Theoretische Physik,Fakultät für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Hassler, Falk [University of North Carolina, Department of Physics and Astronomy,Phillips Hall, CB #3255, 120 E. Cameron Ave., Chapel Hill, NC 27599-3255 (United States); City University of New York, The Graduate Center,365 Fifth Avenue, New York, NY 10016 (United States); Columbia University, Department of Physics,Pupin Hall, 550 West 120th St., New York, NY 10027 (United States); Lüst, Dieter [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Arnold-Sommerfeld-Center für Theoretische Physik,Fakultät für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany)

2016-02-04

A flux formulation of Double Field Theory on group manifold is derived and applied to study generalized Scherk-Schwarz compactifications, which give rise to a bosonic subsector of half-maximal, electrically gauged supergravities. In contrast to the flux formulation of original DFT, the covariant fluxes split into a fluctuation and a background part. The latter is connected to a 2D-dimensional, pseudo Riemannian manifold, which is isomorphic to a Lie group embedded into O(D,D). All fields and parameters of generalized diffeomorphisms are supported on this manifold, whose metric is spanned by the background vielbein E{sub A}{sup I}∈ GL(2D). This vielbein takes the role of the twist in conventional generalized Scherk-Schwarz compactifications. By doing so, it solves the long standing problem of constructing an appropriate twist for each solution of the embedding tensor. Using the geometric structure, absent in original DFT, E{sub A}{sup I} is identified with the left invariant Maurer-Cartan form on the group manifold, in the same way as it is done in geometric Scherk-Schwarz reductions. We show in detail how the Maurer-Cartan form for semisimple and solvable Lie groups is constructed starting from the Lie algebra. For all compact embeddings in O(3,3), we calculate E{sub A}{sup I}.

The eyes don't have it: lie detection and Neuro-Linguistic Programming.

Directory of Open Access Journals (Sweden)

Richard Wiseman

Full Text Available Proponents of Neuro-Linguistic Programming (NLP claim that certain eye-movements are reliable indicators of lying. According to this notion, a person looking up to their right suggests a lie whereas looking up to their left is indicative of truth telling. Despite widespread belief in this claim, no previous research has examined its validity. In Study 1 the eye movements of participants who were lying or telling the truth were coded, but did not match the NLP patterning. In Study 2 one group of participants were told about the NLP eye-movement hypothesis whilst a second control group were not. Both groups then undertook a lie detection test. No significant differences emerged between the two groups. Study 3 involved coding the eye movements of both liars and truth tellers taking part in high profile press conferences. Once again, no significant differences were discovered. Taken together the results of the three studies fail to support the claims of NLP. The theoretical and practical implications of these findings are discussed.

Cross-Cultural Differences in Children’s Choices, Categorizations, and Evaluations of Truths and Lies

Science.gov (United States)

Fu, Genyue; Xu, Fen; Cameron, Catherine Ann; Heyman, Gail; Lee, Kang

2008-01-01

This study examined cross-cultural differences and similarities in children’s moral understanding of individual- or collective-oriented lies and truths. Seven-, 9-, and 11-year-old Canadian and Chinese children were read stories about story characters facing moral dilemmas about whether to lie or tell the truth to help a group but harm an individual or vice versa. Participants chose to lie or to tell the truth as if they were the character (Experiments 1 and 2) and categorized and evaluated the story characters’ truthful and untruthful statements (Experiments 3 and 4). Most children in both cultures labeled lies as lies and truths as truths. The major cultural differences lay in choices and moral evaluations. Chinese children chose lying to help a collective but harm an individual, and they rated it less negatively than lying with opposite consequences. Chinese children rated truth telling to help an individual but harm a group less positively than the alternative. Canadian children did the opposite. These findings suggest that cross-cultural differences in emphasis on groups versus individuals affect children’s choices and moral judgments about truth and deception. PMID:17352539

Rill erosion on an oxisol influenced by a thin compacted layer

Directory of Open Access Journals (Sweden)

Edivaldo Lopes Thomaz

2013-10-01

Full Text Available The presence of compacted layers in soils can induce subprocesses (e.g., discontinuity of water flow and induces soil erosion and rill development. This study assesses how rill erosion in Oxisols is affected by a plow pan. The study shows that changes in hydraulic properties occur when the topsoil is eroded because the compacted layer lies close below the surface. The hydraulic properties that induce sediment transport and rill formation (i.e., hydraulic thresholds at which these processes occur are not the same. Because of the resistance of the compacted layer, the hydraulic conditions leading to rill incision on the soil surface differed from the conditions inducing rill deepening. The Reynolds number was the best hydraulic predictor for both processes. The formed rills were shallow and could easily be removed by tillage between crops. However, during rill development, large amounts of soil and contaminants could also be transferred.

A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation

Science.gov (United States)

Somma, Rolando D.

2016-06-01

We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm with respect to the dimension of the Lie algebra, or when the norm of the effective operator resulting from nested commutators is less than the product of the norms, the number of terms in the product is significantly less than that obtained from well-known results. We apply our results to construct product formulas useful for the quantum simulation of some continuous-variable and bosonic physical systems, including systems whose potential is not quadratic. For many of these systems, we show that the number of terms in the product can be sublinear or even subpolynomial in the dimension of the relevant local Hilbert spaces, where such a dimension is usually determined by the energy scale of the problem. Our results emphasize the power of quantum computers for the simulation of various quantum systems.

Lying in business : Insights from Hanna Arendt's 'Lying in Politics'

NARCIS (Netherlands)

Eenkhoorn, P.; Graafland, J.J.

2011-01-01

The political philosopher Hannah Arendt develops several arguments regarding 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

Solitons, Lie Group Analysis and Conservation Laws of a (3+1)-Dimensional Modified Zakharov-Kuznetsov Equation in a Multicomponent Magnetised Plasma

Science.gov (United States)

Du, Xia-Xia; Tian, Bo; Chai, Jun; Sun, Yan; Yuan, Yu-Qiang

2017-11-01

In this paper, we investigate a (3+1)-dimensional modified Zakharov-Kuznetsov equation, which describes the nonlinear plasma-acoustic waves in a multicomponent magnetised plasma. With the aid of the Hirota method and symbolic computation, bilinear forms and one-, two- and three-soliton solutions are derived. The characteristics and interaction of the solitons are discussed graphically. We present the effects on the soliton's amplitude by the nonlinear coefficients which are related to the ratio of the positive-ion mass to negative-ion mass, number densities, initial densities of the lower- and higher-temperature electrons and ratio of the lower temperature to the higher temperature for electrons, as well as by the dispersion coefficient, which is related to the ratio of the positive-ion mass to the negative-ion mass and number densities. Moreover, using the Lie symmetry group theory, we derive the Lie point symmetry generators and the corresponding symmetry reductions, through which certain analytic solutions are obtained via the power series expansion method and the (G'/G) expansion method. We demonstrate that such an equation is strictly self-adjoint, and the conservation laws associated with the Lie point symmetry generators are derived.

A Compact Group of Galaxies at z = 2.48 Hosting an AGN-driven Outflow

Science.gov (United States)

Shih, Hsin-Yi; Stockton, Alan

2015-12-01

We present observations of a remarkable compact group of galaxies at z = 2.48. Four galaxies, all within 40 kpc of each other, surround a powerful high-redshift radio source. This group comprises two compact red passive galaxies and a pair of merging galaxies. One of the red galaxies, with an apparent stellar mass of 3.6 × 1011M⊙ and an effective radius of 470 pc, is one of the most extreme examples of a massive quiescent compact galaxy found so far. One of the pair of merging galaxies hosts the active galactic nucleus (AGN) producing the large powerful radio structure. The merger is massive and enriched, consistent with the mass-metallicity relation expected at this redshift. Close to the merging nuclei, the emission lines exhibit broad and asymmetric profiles that suggest outflows powered either by a very young expanding radio jet or by AGN radiation. At ≳50 kpc from the system, we found a fainter extended-emission region that may be a part of a radio-jet-driven outflow. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The work is also based, in part, on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan, and on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil), and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina).

Politicians lie, so do I.

Science.gov (United States)

Celse, Jérémy; Chang, Kirk

2017-11-30

This research analyzed whether political leaders make people lie via priming experiments. Priming is a non-conscious and implicit memory effect in which exposure to one stimulus affects the response to another. Following priming theories, we proposed an innovative concept that people who perceive leaders to be dishonest (such as liars) are likely to lie themselves. We designed three experiments to analyze and critically discussed the potential influence of prime effect on lying behavior, through the prime effect of French political leaders (including general politicians, presidents and parties). Experiment 1 discovered that participants with non-politician-prime were less likely to lie (compared to politician-prime). Experiment 2A discovered that, compared to Hollande-prime, Sarkozy-prime led to lying behavior both in gravity (i.e., bigger lies) and frequency (i.e., lying more frequently). Experiment 2B discovered that Republicans-prime yielded an impact on more lying behavior, and Sarkozy-prime made such impact even stronger. Overall, the research findings suggest that lying can be triggered by external influencers such as leaders, presidents and politicians in the organizations. Our findings have provided valuable insights into organizational leaders and managers in their personnel management practice, especially in the intervention of lying behavior. Our findings also have offered new insights to explain non-conscious lying behavior.

Lie detection based on nonverbal expressions - study of the Czech Republic Police employees

Directory of Open Access Journals (Sweden)

Hedvika Boukalová

2014-12-01

Full Text Available Lie detection based on nonverbal behavior is not a standard method, it is an intuitive process, applied by lay persons, but also professionals. Some of the major sources (e.g. widespread Interrogation Manual by F. Inbau et al., 2004 offer clear recommendations about the nonverbal behavior of liars to investigators of serious crime. These findings are not supported by the research, moreover they can lead to lowering the ability to detect lie (Blair, Kooi 2004. Another topic is mapping the skills of professionals (police officers, members of the secret services and non-specialists to detect lies by nonverbal signs. Across the studies (with few exceptions a low performance in the task of detecting lies by nonverbal expressions (Ekman P., 1996; Vrij, 2004 and others is found. The levels of success are usually around the level of chance. The potential reasons for such results are analyzed (e.g. Blair, Kooi, 2004. However a group of psychologists led by P. Ekman and M. O'Sullivan (O'Sullivan, 2007 managed to find in their years lasting research a group of people whose ability to detect lies is well above the population average. This group is diverse in terms of age, interests and professions, all of them come from the USA. There were certain common features found in this group and also a focus on similar phenomena in the detection of lying. The main goal and research question is to find out: what is the success rate of differentiation between lies and truths in this specific professional group of Czech population, is it the same or different from the results reported in the context of available resources. The research will focus on the ability of respondents to determine the truth or deceit on the basis of non-verbal and paraverbal expressions of observed subjects, with focus on specific professional groups - mainly police workers. We assume, that the police officers are frequently in the contact with people, who are not willing to reveal critical

Solution of spatially homogeneous model Boltzmann equations by means of Lie groups of transformations

International Nuclear Information System (INIS)

Foroutan, A.

1992-05-01

The essential mathematical challenge in transport theory is based on the nonlinearity of the integro-differential equations governing classical thermodynamic systems on molecular kinetic level. It is the aim of this thesis to gain exact analytical solutions to the model Boltzmann equation suggested by Tjon and Wu. Such solutions afford a deeper insight into the dynamics of rarefied gases. Tjon and Wu have provided a stochastic model of a Boltzmann equation. Its transition probability depends only on the relative speed of the colliding particles. This assumption leads in the case of two translational degrees of freedom to an integro-differential equation of convolution type. According to this convolution structure the integro-differential equation is Laplace transformed. The result is a nonlinear partial differential equation. The investigation of the symmetries of this differential equation by means of Lie groups of transformation enables us to transform the originally nonlinear partial differential equation into ordinary differential equation into ordinary differential equations of Bernoulli type. (author)

Medicine, lies and deceptions.

Science.gov (United States)

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.

The derivation of the conventional basis for the classical Lie algebra generators

International Nuclear Information System (INIS)

Karadayi, H.R.

1982-01-01

The explicit construction of the classical Lie algebra generators in the conventional Gell-Mann basis is derived for all irreducible unitary representations of all classical groups. The main framework is based on a description of the simple roots of the classical Lie algebras such that the inter-relations implied by the Cartan matrix of the group among these simple roots are explicit within this description. (author)

Computing nilpotent quotients in finitely presented Lie rings

Directory of Open Access Journals (Sweden)

Csaba Schneider

1997-12-01

Full Text Available A nilpotent quotient algorithm for finitely presented Lie rings over Z (and Q is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed by generators. Using that presentation the word problem is decidable in L. Provided that the Lie ring L is graded, it is possible to determine the canonical presentation for a lower central factor of L. Complexity is studied and it is shown that optimising the presentation is NP-hard. Computational details are provided with examples, timing and some structure theorems obtained from computations. Implementation in C and GAP interface are available.

Particle-like structure of Lie algebras

Science.gov (United States)

Vinogradov, A. M.

2017-07-01

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

Binding lies

Directory of Open Access Journals (Sweden)

Avraham eMerzel

2015-10-01

Full Text Available Do we feel bound by our own misrepresentations? Does one act of cheating compel the cheater to make subsequent choices that maintain the false image even at a cost? To answer these questions we employed a two-task paradigm such that in the first task the participants could benefit from false reporting of private observations whereas in the second they could benefit from making a prediction in line with their actual, rather than their previously reported observations. Thus, for those participants who inflated their report during the first task, sticking with that report for the second task was likely to lead to a loss, whereas deviating from it would imply that they had lied. Data from three experiments (total N=116 indicate that, having lied, participants were ready to suffer future loss rather than admit, even if implicitly, that they had lied.

When is a lie acceptable? Work and private life lying acceptance depends on its beneficiary.

Science.gov (United States)

Cantarero, Katarzyna; Szarota, Piotr; Stamkou, Eftychia; Navas, Marisol; Dominguez Espinosa, Alejandra Del Carmen

2018-01-01

In this article we show that when analyzing attitude towards lying in a cross-cultural setting, both the beneficiary of the lie (self vs other) and the context (private life vs. professional domain) should be considered. In a study conducted in Estonia, Ireland, Mexico, The Netherlands, Poland, Spain, and Sweden (N = 1345), in which participants evaluated stories presenting various types of lies, we found usefulness of relying on the dimensions. Results showed that in the joint sample the most acceptable were other-oriented lies concerning private life, then other-oriented lies in the professional domain, followed by egoistic lies in the professional domain; and the least acceptance was shown for egoistic lies regarding one's private life. We found a negative correlation between acceptance of a behavior and the evaluation of its deceitfulness.

Lie algebraical aspects of quantum statistics

International Nuclear Information System (INIS)

Palev, T.D.

1976-01-01

It is shown that the secon quantization axioms can, in principle, be satisfied with creation and annihilation operators generating (in the case of n pairs of such operators) the Lie algebra Asub(n) of the group SL(n+1). A concept of the Fock space is introduced. The matrix elements of the operators are found

A cohomological characterization of Leibniz central extensions of Lie algebras

International Nuclear Information System (INIS)

Hu Naihong; Pei Yufeng; Liu Dong

2006-12-01

Motivated by Pirashvili's spectral sequences on a Leibniz algebra, some notions such as invariant symmetric bilinear forms, dual space derivations and the Cartan-Koszul homomorphism are connected together to give a description of the second Leibniz cohomology groups with trivial coefficients of Lie algebras (as Leibniz objects), which leads to a concise approach to determining one-dimensional Leibniz central extensions of Lie algebras. As applications, we contain the discussions for some interesting classes of infinite-dimensional Lie algebras. In particular, our results include the cohomological version of Gao's main Theorem for Kac-Moody algebras and answer a question. (author)

Verbal lie detection

NARCIS (Netherlands)

Vrij, Aldert; Taylor, Paul J.; Picornell, Isabel; Oxburgh, Gavin; Myklebust, Trond; Grant, Tim; Milne, Rebecca

2015-01-01

In this chapter, we discuss verbal lie detection and will argue that speech content can be revealing about deception. Starting with a section discussing the, in our view, myth that non-verbal behaviour would be more revealing about deception than speech, we then provide an overview of verbal lie

LIE n-RACKS

OpenAIRE

Biyogmam, Guy Roger

2011-01-01

In this paper, we introduce the category of Lie $n$-racks and generalize several results known on racks. In particular, we show that the tangent space of a Lie $n$-Rack at the neutral element has a Leibniz $n$-algebra structure. We also define a cohomology theory of $n$-racks..

Matrix groups for undergraduates

CERN Document Server

Tapp, Kristopher

2016-01-01

Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe the basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, maximal tori, homogeneous spaces, and roots. This second edition includes two new chapters that allow for an easier transition to the general theory of Lie groups. From reviews of the First Edition: This book could be used as an excellent textbook for a one semester course at university and it will prepare students for a graduate course on Lie groups, Lie algebras, etc. … The book combines an intuitive style of writing w...

Nonflexible Lie-admissible algebras

International Nuclear Information System (INIS)

Myung, H.C.

1978-01-01

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

Élie Cartan (1869-1951)

CERN Document Server

Akivis, M A

2011-01-01

This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.

Stellar Populations in Compact Galaxy Groups: a Multi-wavelength Study of HCGs 16, 22, and 42, Their Star Clusters, and Dwarf Galaxies

Science.gov (United States)

Konstantopoulos, I. S.; Maybhate, A.; Charlton, J. C.; Fedotov, K.; Durrell, P. R.; Mulchaey, J. S.; English, J.; Desjardins, T. D.; Gallagher, S. C.; Walker, L. M.;

Isomorphism of Intransitive Linear Lie Equations

Directory of Open Access Journals (Sweden)

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.

Filiform Lie algebras of order 3

Science.gov (United States)

Navarro, R. M.

2014-04-01

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

When is a lie more of a lie? Moral judgment mediates the relationship between perceived benefits of others and lie-labeling

Directory of Open Access Journals (Sweden)

Cantarero Katarzyna

2017-06-01

Full Text Available Lay perceptions of lying are argued to consist of a lie prototype. The latter was found to entail the intention to deceive, belief in falsity and falsity (Coleman & Kay, 1981. We proposed and found that the perceptions of the benefits of others are also an important factor that influences the extent, to which an act of intentional misleading someone to foster a false belief is labeled as a lie. Drawing from the intuitionist model of moral judgments (Haidt, 2001 we assumed that moral judgment of the behaviour would mediate the relationship. In Study 1 we analyzed data coming from a crosscultural project and found that perceived intention to benefit others was negatively related to lie labeling and that this relationship was mediated by the moral judgment of that act. In Study 2 we found that manipulating the benefits of others influenced the extent, to which an act of intentional misleading in order to foster a false belief is labeled as a lie and that, again, this relationship is mediated by the moral judgment of that act.

Lie Algebras and Integrable Systems

International Nuclear Information System (INIS)

Zhang Yufeng; Mei Jianqin

2012-01-01

A 3 × 3 matrix Lie algebra is first introduced, its subalgebras and the generated Lie algebras are obtained, respectively. Applications of a few Lie subalgebras give rise to two integrable nonlinear hierarchies of evolution equations from their reductions we obtain the nonlinear Schrödinger equations, the mKdV equations, the Broer-Kaup (BK) equation and its generalized equation, etc. The linear and nonlinear integrable couplings of one integrable hierarchy presented in the paper are worked out by casting a 3 × 3 Lie subalgebra into a 2 × 2 matrix Lie algebra. Finally, we discuss the elliptic variable solutions of a generalized BK equation. (general)

873rd Meeting of the American Mathematical Society on Lie Algebras, Cohomology and New Applications to Quantum Mechanics

CERN Document Server

Olver, Peter J; the American Mathematical Society on Lie Algebras, Cohomology and New Applications to Quantum Mechanics

1994-01-01

This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrödinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, p...

High-Quality Ultra-Compact Grid Layout of Grouped Networks.

Science.gov (United States)

Yoghourdjian, Vahan; Dwyer, Tim; Gange, Graeme; Kieffer, Steve; Klein, Karsten; Marriott, Kim

2016-01-01

Prior research into network layout has focused on fast heuristic techniques for layout of large networks, or complex multi-stage pipelines for higher quality layout of small graphs. Improvements to these pipeline techniques, especially for orthogonal-style layout, are difficult and practical results have been slight in recent years. Yet, as discussed in this paper, there remain significant issues in the quality of the layouts produced by these techniques, even for quite small networks. This is especially true when layout with additional grouping constraints is required. The first contribution of this paper is to investigate an ultra-compact, grid-like network layout aesthetic that is motivated by the grid arrangements that are used almost universally by designers in typographical layout. Since the time when these heuristic and pipeline-based graph-layout methods were conceived, generic technologies (MIP, CP and SAT) for solving combinatorial and mixed-integer optimization problems have improved massively. The second contribution of this paper is to reassess whether these techniques can be used for high-quality layout of small graphs. While they are fast enough for graphs of up to 50 nodes we found these methods do not scale up. Our third contribution is a large-neighborhood search meta-heuristic approach that is scalable to larger networks.

Automated decoding of facial expressions reveals marked differences in children when telling antisocial versus prosocial lies.

Science.gov (United States)

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.

Filiform Lie algebras of order 3

International Nuclear Information System (INIS)

Navarro, R. M.

2014-01-01

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

On lying and deceiving.

OpenAIRE

Bakhurst, D

1992-01-01

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 misconstrue...

THE WHIQII SURVEY: METALLICITIES AND SPECTROSCOPIC PROPERTIES OF LUMINOUS COMPACT BLUE GALAXIES

International Nuclear Information System (INIS)

Tollerud, Erik J.; Barton, Elizabeth J.; Cooke, Jeff; Van Zee, Liese

2010-01-01

As part of the WIYN High Image Quality Indiana-Irvine (WHIQII) survey, we present 123 spectra of faint emission-line galaxies, selected to focus on intermediate redshift (0.4 ∼ 23 -O 32 plane that differs from luminous local galaxies and is more consistent with dwarf irregulars at the present epoch, suggesting that cosmic 'downsizing' is observable in even the most fundamental parameters that describe star formation. These properties for our sample are also generally consistent with lying between local galaxies and those at high redshift, as expected by this scenario. Surprisingly, our sample exhibits no detectable correlation between compactness and metallicity, strongly suggesting that at these epochs of rapid star formation, the morphology of compact star-forming galaxies is largely transient.

Strong far-infrared cooling lines, peculiar CO kinematics, and possible star-formation suppression in Hickson compact group 57

DEFF Research Database (Denmark)

Alatalo, K.; Appleton, P. N.; Lisenfeld, U.

2014-01-01

We present [C II] and [O I] observations from Herschel and CO(1-0) maps from the Combined Array for Research in Millimeter Astronomy (CARMA) of the Hickson compact group HCG 57, focusing on the galaxies HCG 57a and HCG 57d. HCG 57a has been previously shown to contain enhanced quantities of warm ...

Computations in finite-dimensional Lie algebras

Directory of Open Access Journals (Sweden)

A. M. Cohen

1997-12-01

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

Lying in Business : Insights from Hannah Arendt’s ‘Lying in Politics’

NARCIS (Netherlands)

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

Lying relies on the truth

NARCIS (Netherlands)

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

Lie families: theory and applications

International Nuclear Information System (INIS)

Carinena, Jose F; Grabowski, Janusz; De Lucas, Javier

2010-01-01

We analyze the families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e. a time-dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants. We next study the relations of these families, called Lie families, with the theory of Lie and quasi-Lie systems and apply our theory to provide common time-dependent superposition rules for certain Lie families.

On Lie point symmetry of classical Wess-Zumino-Witten model

International Nuclear Information System (INIS)

Maharana, Karmadeva

2001-06-01

We perform the group analysis of Witten's equations of motion for a particle moving in the presence of a magnetic monopole, and also when constrained to move on the surface of a sphere, which is the classical example of Wess-Zumino-Witten model. We also consider variations of this model. Our analysis gives the generators of the corresponding Lie point symmetries. The Lie symmetry corresponding to Kepler's third law is obtained in two related examples. (author)

Poisson-Lie T-duality open strings and D-branes

CERN Document Server

Klimcik, C.

1996-01-01

Global issues of the Poisson-Lie T-duality are addressed. It is shown that oriented open strings propagating on a group manifold G are dual to D-brane - anti-D-brane pairs propagating on the dual group manifold \\ti G. The D-branes coincide with the symplectic leaves of the standard Poisson structure induced on the dual group \\ti G by the dressing action of the group G. T-duality maps the momentum of the open string into the mutual distance of the D-branes in the pair. The whole picture is then extended to the full modular space M(D) of the Poisson-Lie equivalent \\si-models which is the space of all Manin triples of a given Drinfeld double.T-duality rotates the zero modes of pairs of D-branes living on targets belonging to M(D). In this more general case the D-branes are preimages of symplectic leaves in certain Poisson homogeneous spaces of their targets and, as such, they are either all even or all odd dimensional.

Purposes and Effects of Lying.

Science.gov (United States)

Hample, Dale

Three exploratory studies were aimed at describing the purposes of lies and the consequences of lying. Data were collected through a partly open-ended questionnaire, a content analysis of several tape-recorded interviews, and a large-scale survey. The results showed that two of every three lies were told for selfish reasons, while three of every…

Teaching the Truth about Lies to Psychology Students: The Speed Lying Task

Science.gov (United States)

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…

The low-lying quartet electronic states of group 14 diatomic borides XB (X = C, Si, Ge, Sn, Pb)

Science.gov (United States)

Pontes, Marcelo A. P.; de Oliveira, Marcos H.; Fernandes, Gabriel F. S.; Da Motta Neto, Joaquim D.; Ferrão, Luiz F. A.; Machado, Francisco B. C.

2018-04-01

The present work focuses in the characterization of the low-lying quartet electronic and spin-orbit states of diatomic borides XB, in which X is an element of group 14 (C, Si, Ge, Sn, PB). The wavefunction was obtained at the CASSCF/MRCI level with a quintuple-ζ quality basis set. Scalar relativistic effects were also taken into account. A systematic and comparative analysis of the spectroscopic properties for the title molecular series was carried out, showing that the (1)4Π→X4Σ- transition band is expected to be measurable by emission spectroscopy to the GeB, SnB and PbB molecules, as already observed for the lighter CB and SiB species.

On lying and deceiving.

Science.gov (United States)

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.

The ease of lying

NARCIS (Netherlands)

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

Matrix groups for undergraduates

CERN Document Server

Tapp, Kristopher

2005-01-01

Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups. Matrix Groups for Undergraduates is concrete and example-driven, with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.

STELLAR POPULATIONS IN COMPACT GALAXY GROUPS: A MULTI-WAVELENGTH STUDY OF HCGs 16, 22, AND 42, THEIR STAR CLUSTERS, AND DWARF GALAXIES

International Nuclear Information System (INIS)

Konstantopoulos, I. S.; Maybhate, A.; Charlton, J. C.; Gronwall, C.; Fedotov, K.; Desjardins, T. D.; Gallagher, S. C.; Durrell, P. R.; Mulchaey, J. S.; English, J.; Walker, L. M.; Johnson, K. E.; Tzanavaris, P.

2013-01-01

We present a multi-wavelength analysis of three compact galaxy groups, Hickson compact groups (HCGs) 16, 22, and 42, which describe a sequence in terms of gas richness, from space- (Swift, Hubble Space Telescope (HST), and Spitzer) and ground-based (Las Campanas Observatory and Cerro Tololo Inter-American Observatory) imaging and spectroscopy. We study various signs of past interactions including a faint, dusty tidal feature about HCG 16A, which we tentatively age-date at <1 Gyr. This represents the possible detection of a tidal feature at the end of its phase of optical observability. Our HST images also resolve what were thought to be double nuclei in HCG 16C and D into multiple, distinct sources, likely to be star clusters. Beyond our phenomenological treatment, we focus primarily on contrasting the stellar populations across these three groups. The star clusters show a remarkable intermediate-age population in HCG 22, and identify the time at which star formation was quenched in HCG 42. We also search for dwarf galaxies at accordant redshifts. The inclusion of 33 members and 27 ''associates'' (possible members) radically changes group dynamical masses, which in turn may affect previous evolutionary classifications. The extended membership paints a picture of relative isolation in HCGs 16 and 22, but shows HCG 42 to be part of a larger structure, following a dichotomy expected from recent studies. We conclude that (1) star cluster populations provide an excellent metric of evolutionary state, as they can age-date the past epochs of star formation; and (2) the extended dwarf galaxy population must be considered in assessing the dynamical state of a compact group.

Freestall maintenance: effects on lying behavior of dairy cattle.

Science.gov (United States)

Drissler, M; Gaworski, M; Tucker, C B; Weary, D M

2005-07-01

In a series of 3 experiments, we documented how sand-bedding depth and distribution changed within freestalls after new bedding was added and the effect of these changes on lying behavior. In experiment 1, we measured changes in bedding depth over a 10-d period at 43 points in 24 freestalls. Change in depth of sand was the greatest the day after new sand was added and decreased over time. Over time, the stall surface became concave, and the deepest part of the stall was at the center. Based on the results of experiment 1, we measured changes in lying behavior when groups of cows had access to freestalls with sand bedding that was 0, 3.5, 5.2, or 6.2 cm at the deepest point, below the curb, while other dimensions remained fixed. We found that daily lying time was 1.15 h shorter in stalls with the lowest levels of bedding compared with stalls filled with bedding. Indeed, for every 1-cm decrease in bedding, cows spent 11 min less time lying down during each 24-h period. In a third experiment, we imposed 4 treatments that reflected the variation in sand depth within stalls: 0, 6.2, 9.9, and 13.7 cm below the curb. Again, lying times reduced with decreasing bedding, such that cows using the stalls with the least amount of bedding (13.7 cm below curb) spent 2.33 h less time per day lying down than when housed with access to freestalls filled with sand (0 cm below curb).

Lie algebras and applications

CERN Document Server

Iachello, Francesco

2015-01-01

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

On lying and deceiving.

Science.gov (United States)

Bakhurst, D

1992-01-01

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. PMID:1619626

Lie and conditional symmetries of the three-component diffusive Lotka–Volterra system

International Nuclear Information System (INIS)

Cherniha, Roman; Davydovych, Vasyl’

2013-01-01

Lie and Q-conditional symmetries of the classical three-component diffusive Lotka–Volterra system in the case of one space variable are studied. The group-classification problems for finding Lie symmetries and Q-conditional symmetries of the first type are completely solved. Notably, non-Lie symmetries (Q-conditional symmetry operators) for a multi-component nonlinear reaction–diffusion system are constructed for the first time. The results are compared with those derived for the two-component diffusive Lotka–Volterra system. The conditional symmetry obtained for the non-Lie reduction of the three-component system used for modeling competition between three species in population dynamics is applied and the relevant exact solutions are found. Particularly, the exact solution describing different scenarios of competition between three species is constructed. (paper)

Noether and Lie symmetries for charged perfect fluids

International Nuclear Information System (INIS)

Kweyama, M C; Govinder, K S; Maharaj, S D

2011-01-01

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.

Duality results for co-compact Gabor systems

DEFF Research Database (Denmark)

Jakobsen, Mads Sielemann; Lemvig, Jakob

2015-01-01

In this paper we give an account of recent developments in the duality theory of Gabor frames. We prove the Wexler-Raz biorthogonality relations and the duality principle for co-compact Gabor systems on second countable, locally compact abelian groups G. Our presentation does not rely on the exis...

Integral dimension in the string theory based on a group manifold

International Nuclear Information System (INIS)

Toyota, N.

1990-01-01

We study string models on a group manifold with Kac-Moody symmetry where the critical dimension d is integer. In particular the possibility of four-dimensional models is investigated. We find that only nine group manifolds with a relevant k level can have four as the critical dimension among an infinite number of compact Lie groups. They are all listed. The models with minimal conformal sectors adding to the Kac-Moody sector are investigated. In the cases with minimal conformal sector, there are only two groups, SU(5) and SO(43), that can give d=4. Among the cases with some tensoring products of minimal conformal sectors we discuss a few special cases with k=0 and k=1. The cases based on N=1 super Kac-Moody algebra are also studied. Finally we discuss the possibility of the enlargement of gauge symmetry. (orig.)

Lie algebra of conformal Killing–Yano forms

International Nuclear Information System (INIS)

Ertem, Ümit

2016-01-01

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

Fractional supersymmetry and infinite dimensional lie algebras

International Nuclear Information System (INIS)

Rausch de Traubenberg, M.

2001-01-01

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

Symmetries and groups in particle physics; Symmetrien und Gruppen in der Teilchenphysik

Energy Technology Data Exchange (ETDEWEB)

Scherer, Stefan [Mainz Univ. (Germany)

2016-07-01

The aim of this book consists of a didactic introduction to the group-theoretical considerations and methods, which have led to an ever deeper understanding of the interactions of the elementary particles. The first three chapters deal primarily with the foundations of the representation theory of primarily finite groups, whereby many results are also transferable to compact Lie groups. In the third chapter we discuss the concept of Lie groups and their connection with Lie algebras. In the remaining chapter it is mainly about the application of group theory in physics. Chapter 4 deals with the groups SO(3) and SU(2), which occur in connection with the description of the angular momentum in quantum mechanics. We discuss the Wigner-Eckar theorem together with some applications. In chapter 5 we are employed to the composition properties of strongly interacting systems, so called hadrons, and discuss extensively the transformation properties of quarks with relation to the special unitary groups. The Noether theorem is generally treated in connection to the conservation laws belonging to the Galilei group and the Poincare group. We confine us in chapter 6 to internal symmetries, but explain for that extensively the application to quantum field theory. Especially an outlook on the effect of symmetries in form of so called Ward identities is granted. In chapter 7 we turn towards the gauge principle and discuss first the construction of quantum electrodynamics. In the following we generalize the gauge principle to non-Abelian groups (Yang-Mills theories) and formulate the quantum chromodynamics (QCD). Especially we take a view of ''random'' global symmetries of QCD, especially the chiral symmetry. In chapter 8 we illuminate the phenomenon of spontaneous symmetry breaking both for global and for local symmetries. In the final chapter we work out the group-theoretical structure of the Standard Model. Finally by means of the group SU(5) we take a view to

Cross-Cultural Differences in Children's Choices, Categorizations, and Evaluations of Truths and Lies

Science.gov (United States)

Fu, Genyue; Xu, Fen; Cameron, Catherine Ann; Leyman, Gail; Lee, Kang

2007-01-01

This study examined cross-cultural differences and similarities in children's moral understanding of individual- or collective-oriented lies and truths. Seven-, 9-, and 11-year-old Canadian and Chinese children were read stories about story characters facing moral dilemmas about whether to lie or tell the truth to help a group but harm an…

Invariants of triangular Lie algebras

International Nuclear Information System (INIS)

Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

2007-01-01

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

Harmonic Analysis and Group Representation

CERN Document Server

Figa-Talamanca, Alessandro

2011-01-01

This title includes: Lectures - A. Auslander, R. Tolimeri - Nilpotent groups and abelian varieties, M Cowling - Unitary and uniformly bounded representations of some simple Lie groups, M. Duflo - Construction de representations unitaires d'un groupe de Lie, R. Howe - On a notion of rank for unitary representations of the classical groups, V.S. Varadarajan - Eigenfunction expansions of semisimple Lie groups, and R. Zimmer - Ergodic theory, group representations and rigidity; and, Seminars - A. Koranyi - Some applications of Gelfand pairs in classical analysis.

A unified approach to the minimal unitary realizations of noncompact groups and supergroups

International Nuclear Information System (INIS)

Guenaydin, Murat; Pavlyk, Oleksandr

2006-01-01

We study the minimal unitary representations of non-compact groups and supergroups obtained by quantization of their geometric realizations as quasi-conformal groups and supergroups. The quasi-conformal groups G leave generalized light-cones defined by a quartic norm invariant and have maximal rank subgroups of the form H x SL(2, R) such that G/H x SL(2, R) are para-quaternionic symmetric spaces. We give a unified formulation of the minimal unitary representations of simple non-compact groups of type A 2 , G 2 , D 4 , F 4 , E 6 , E 7 , E 8 and Sp(2n, R). The minimal unitary representations of Sp(2n, R) are simply the singleton representations and correspond to a degenerate limit of the unified construction. The minimal unitary representations of the other noncompact groups SU(m, n), SO(m, n), SO*(2n) and SL(m, R) are also given explicitly. We extend our formalism to define and construct the corresponding minimal representations of non-compact supergroups G whose even subgroups are of the form H x SL(2, R). If H is noncompact then the supergroup G does not admit any unitary representations, in general. The unified construction with H simple or Abelian leads to the minimal representations of G(3), F(4) and O Sp(n|2, R) (in the degenerate limit). The minimal unitary representations of O Sp(n|2, R) with even subgroups SO(n) x SL(2, R) are the singleton representations. We also give the minimal realization of the one parameter family of Lie superalgebras D(2, 1; σ)

Lie algebroids in derived differential topology

NARCIS (Netherlands)

Nuiten, J.J.

2018-01-01

A classical principle in deformation theory asserts that any formal deformation problem is controlled by a differential graded Lie algebra. This thesis studies a generalization of this principle to Lie algebroids, and uses this to examine the interactions between the theory of Lie algebroids and the

Quantum Lie theory a multilinear approach

CERN Document Server

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.

BRST-operator for quantum Lie algebra and differential calculus on quantum groups

International Nuclear Information System (INIS)

Isaev, A.P.; Ogievetskij, O.V.

2001-01-01

For A Hopf algebra one determined structure of differential complex in two dual external Hopf algebras: A external expansion and in A* dual algebra external expansion. The Heisenberg double of these two Hopf algebras governs the differential algebra for the Cartan differential calculus on A algebra. The forst differential complex is the analog of the de Rame complex. The second complex coincide with the standard complex. Differential is realized as (anti)commutator with Q BRST-operator. Paper contains recursion relation that determines unequivocally Q operator. For U q (gl(N)) Lie quantum algebra one constructed BRST- and anti-BRST-operators and formulated the theorem of the Hodge expansion [ru

The Relative Lie Algebra Cohomology of the Weil Representation

Science.gov (United States)

Ralston, Jacob

We study the relative Lie algebra cohomology of so(p,q) with values in the Weil representation piof the dual pair Sp(2k, R) x O(p,q ). Using the Fock model defined in Chapter 2, we filter this complex and construct the associated spectral sequence. We then prove that the resulting spectral sequence converges to the relative Lie algebra cohomology and has E0 term, the associated graded complex, isomorphic to a Koszul complex, see Section 3.4. It is immediate that the construction of the spectral sequence of Chapter 3 can be applied to any reductive subalgebra g ⊂ sp(2k(p + q), R). By the Weil representation of O( p,|q), we mean the twist of the Weil representation of the two-fold cover O(pq)[special character omitted] by a suitable character. We do this to make the center of O(pq)[special character omitted] act trivially. Otherwise, all relative Lie algebra cohomology groups would vanish, see Proposition 4.10.2. In case the symplectic group is large relative to the orthogonal group (k ≥ pq), the E 0 term is isomorphic to a Koszul complex defined by a regular sequence, see 3.4. Thus, the cohomology vanishes except in top degree. This result is obtained without calculating the space of cochains and hence without using any representation theory. On the other hand, in case k BMR], this author wrote with his advisor John Millson and Nicolas Bergeron of the University of Paris.

Algebraic Bethe ansatz for U(1) invariant integrable models: Compact and non-compact applications

International Nuclear Information System (INIS)

Martins, M.J.; Melo, C.S.

2009-01-01

We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U q [SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the SL(2,R) algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact SL(2,R) model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact SL(2,R) model starting from systems with finite degrees of freedom.

Algebraic Bethe ansatz for U(1) invariant integrable models: Compact and non-compact applications

Science.gov (United States)

Martins, M. J.; Melo, C. S.

2009-10-01

We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U[SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the SL(2,R) algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact SL(2,R) model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact SL(2,R) model starting from systems with finite degrees of freedom.

Analysis of laboratory compaction methods of roller compacted concrete

Science.gov (United States)

Trtík, Tomáš; Chylík, Roman; Bílý, Petr; Fládr, Josef

2017-09-01

Roller-Compacted Concrete (RCC) is an ordinary concrete poured and compacted with machines typically used for laying of asphalt road layers. One of the problems connected with this technology is preparation of representative samples in the laboratory. The aim of this work was to analyse two methods of preparation of RCC laboratory samples with bulk density as the comparative parameter. The first method used dynamic compaction by pneumatic hammer. The second method of compaction had a static character. The specimens were loaded by precisely defined force in laboratory loading machine to create the same conditions as during static rolling (in the Czech Republic, only static rolling is commonly used). Bulk densities obtained by the two compaction methods were compared with core drills extracted from real RCC structure. The results have shown that the samples produced by pneumatic hammer tend to overestimate the bulk density of the material. For both compaction methods, immediate bearing index test was performed to verify the quality of compaction. A fundamental difference between static and dynamic compaction was identified. In static compaction, initial resistance to penetration of the mandrel was higher, after exceeding certain limit the resistance was constant. This means that the samples were well compacted just on the surface. Specimens made by pneumatic hammer actively resisted throughout the test, the whole volume was uniformly compacted.

Vertex ring-indexed Lie algebras

International Nuclear Information System (INIS)

Fairlie, David; Zachos, Cosmas

2005-01-01

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

Classification of simple flexible Lie-admissible algebras

International Nuclear Information System (INIS)

Okubo, S.; Myung, H.C.

1979-01-01

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

Continuum analogues of contragredient Lie algebras

International Nuclear Information System (INIS)

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

1989-03-01

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

PROPERTIES OF THE COMPACT H II REGION COMPLEX G-0.02-0.07

International Nuclear Information System (INIS)

Mills, E.; Morris, M. R.; Lang, C. C.; Dong, H.; Wang, Q. D.; Cotera, A.; Stolovy, S. R.

2011-01-01

We present new extinction maps and high-resolution Paschen-alpha images of G-0.02-0.07, a complex of compact H II regions located adjacent to the M-0.02-0.07 giant molecular cloud, 6 pc in projection from the center of the Galaxy. These H II regions, which lie in projection just outside the boundary of the Sgr A East supernova remnant, represent one of the most recent episodes of star formation in the central parsecs of the Galaxy. The 1.87 μm extinctions of regions A, B, and C are almost identical, approximately 3.7 mag. Region D, in contrast, has a peak extinction of A 1.87 = 5.9 mag. Adopting an extinction law specific to the Galactic center, we find that these extinctions correspond to visual extinctions of A V = 45 and A V = 71. The similar and uniform extinctions of regions A, B, and C are consistent with that expected for foreground extinction in the direction of the Galactic center, suggesting that they lie at the front side of the M-0.02-0.07 molecular cloud. Region D is more compact, has a higher extinction, and is thus suspected to be younger and embedded in a dense core in a compressed ridge on the western edge of this cloud.

Lying in neuropsychology.

Science.gov (United States)

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. Copyright © 2014. Published by Elsevier SAS.

Lie-algebra approach to symmetry breaking

International Nuclear Information System (INIS)

Anderson, J.T.

1981-01-01

A formal Lie-algebra approach to symmetry breaking is studied in an attempt to reduce the arbitrariness of Lagrangian (Hamiltonian) models which include several free parameters and/or ad hoc symmetry groups. From Lie algebra it is shown that the unbroken Lagrangian vacuum symmetry can be identified from a linear function of integers which are Cartan matrix elements. In broken symmetry if the breaking operators form an algebra then the breaking symmetry (or symmetries) can be identified from linear functions of integers characteristic of the breaking symmetries. The results are applied to the Dirac Hamiltonian of a sum of flavored fermions and colored bosons in the absence of dynamical symmetry breaking. In the partially reduced quadratic Hamiltonian the breaking-operator functions are shown to consist of terms of order g 2 , g, and g 0 in the color coupling constants and identified with strong (boson-boson), medium strong (boson-fermion), and fine-structure (fermion-fermion) interactions. The breaking operators include a boson helicity operator in addition to the familiar fermion helicity and ''spin-orbit'' terms. Within the broken vacuum defined by the conventional formalism, the field divergence yields a gauge which is a linear function of Cartan matrix integers and which specifies the vacuum symmetry. We find that the vacuum symmetry is chiral SU(3) x SU(3) and the axial-vector-current divergence gives a PCAC -like function of the Cartan matrix integers which reduces to PCAC for SU(2) x SU(2) breaking. For the mass spectra of the nonets J/sup P/ = 0 - ,1/2 + ,1 - the integer runs through the sequence 3,0,-1,-2, which indicates that the breaking subgroups are the simple Lie groups. Exact axial-vector-current conservation indicates a breaking sum rule which generates octet enhancement. Finally, the second-order breaking terms are obtained from the second-order spin tensor sum of the completely reduced quartic Hamiltonian

The First Honest Book about Lies.

Science.gov (United States)

Kincher, Jonni; Espeland, Pamela, Ed.

Readers learn how to discern the truth from lies through a series of activities, games, and experiments. This book invites young students to look at lies in a fair and balanced way. Different types of lies are examined and the purposes they serve and discussed. Problem solving activities are given. The book is organized in nine chapters,…

Spontaneous Scalarization of Black Holes and Compact Stars from a Gauss-Bonnet Coupling.

Science.gov (United States)

Silva, Hector O; Sakstein, Jeremy; Gualtieri, Leonardo; Sotiriou, Thomas P; Berti, Emanuele

2018-03-30

We identify a class of scalar-tensor theories with coupling between the scalar and the Gauss-Bonnet invariant that exhibit spontaneous scalarization for both black holes and compact stars. In particular, these theories formally admit all of the stationary solutions of general relativity, but these are not dynamically preferred if certain conditions are satisfied. Remarkably, black holes exhibit scalarization if their mass lies within one of many narrow bands. We find evidence that scalarization can occur in neutron stars as well.

On Deformations and Contractions of Lie Algebras

Directory of Open Access Journals (Sweden)

Marc de Montigny

2006-05-01

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

A linearization of quantum channels

Science.gov (United States)

Crowder, Tanner

2015-06-01

Because the quantum channels form a compact, convex set, we can express any quantum channel as a convex combination of extremal channels. We give a Euclidean representation for the channels whose inverses are also valid channels; these are a subset of the extreme points. They form a compact, connected Lie group, and we calculate its Lie algebra. Lastly, we calculate a maximal torus for the group and provide a constructive approach to decomposing any invertible channel into a product of elementary channels.

The Fourier U(2 Group and Separation of Discrete Variables

Directory of Open Access Journals (Sweden)

Kurt Bernardo Wolf

2011-06-01

Full Text Available The linear canonical transformations of geometric optics on two-dimensional screens form the group Sp(4,R, whose maximal compact subgroup is the Fourier group U(2_F; this includes isotropic and anisotropic Fourier transforms, screen rotations and gyrations in the phase space of ray positions and optical momenta. Deforming classical optics into a Hamiltonian system whose positions and momenta range over a finite set of values, leads us to the finite oscillator model, which is ruled by the Lie algebra so(4. Two distinct subalgebra chains are used to model arrays of N^2 points placed along Cartesian or polar (radius and angle coordinates, thus realizing one case of separation in two discrete coordinates. The N^2-vectors in this space are digital (pixellated images on either of these two grids, related by a unitary transformation. Here we examine the unitary action of the analogue Fourier group on such images, whose rotations are particularly visible.

Time-lapse imagery of Adélie penguins reveals differential winter strategies and breeding site occupation.

Science.gov (United States)

Black, Caitlin; Southwell, Colin; Emmerson, Louise; Lunn, Daniel; Hart, Tom

2018-01-01

Polar seabirds adopt different over-wintering strategies to survive and build condition during the critical winter period. Penguin species either reside at the colony during the winter months or migrate long distances. Tracking studies and survey methods have revealed differences in winter migration routes among penguin species and colonies, dependent on both biotic and abiotic factors present. However, scan sampling methods are rarely used to reveal non-breeding behaviors during winter and little is known about presence at the colony site over this period. Here we show that Adélie penguins on the Yalour Islands in the Western Antarctic Peninsula (WAP) are present year-round at the colony and undergo a mid-winter peak in abundance during winter. We found a negative relationship between daylight hours and penguin abundance when either open water or compact ice conditions were present, suggesting that penguins return to the breeding colony when visibility is lowest for at-sea foraging and when either extreme low or high levels of sea ice exist offshore. In contrast, Adélie penguins breeding in East Antarctica were not observed at the colonies during winter, suggesting that Adélie penguins undergo differential winter strategies in the marginal ice zone on the WAP compared to those in East Antarctica. These results demonstrate that cameras can successfully monitor wildlife year-round in areas that are largely inaccessible during winter.

Unicorns or Tiger Woods: are lie detection experts myths or rarities? A response to on lie detection "wizards" by Bond and Uysal.

Science.gov (United States)

O'Sullivan, Maureen

2007-02-01

Bond and Uysal (this issue) complain that expert lie detectors identified by O'Sullivan and Ekman (2004) are statistical flukes. They ignore one class of experts we have identified and misrepresent the procedures we use to identify the others. They also question the psychometric validity of the measures and protocol used. Many of their points are addressed in the chapter they criticize. The fruitfulness of the O'Sullivan-Ekman protocol is illustrated with respect to improved identification of expert lie detectors, as well as a replicated pattern of errors made by experts from different professional groups. The statistical arguments offered confuse the theoretical use of the binomial with the empirical use of the normal distribution. Data are provided that may clarify this distinction.

Compaction of a Bacterial Group I Ribozyme Coincides with the Assembly of Core Helices

International Nuclear Information System (INIS)

Perez-Salas, U.; Rangan, P.; Krueger, S.; Briber, R.; Thirumalai, D.; Woodson, S.

2004-01-01

Counterions are critical to the self-assembly of RNA tertiary structure because they neutralize the large electrostatic forces which oppose the folding process. Changes in the size and shape of the Azoarcus group I ribozyme as a function of Mg 2+ and Na + concentration were followed by small angle neutron scattering. In low salt buffer, the RNA was expanded, with an average radius of gyration (R g ) of 53 ± 1 Angstroms. A highly cooperative transition to a compact form (R g = 31.5 ± 0.5 Angstroms) was observed between 1.6 and 1.7 mM MgCl 2 . The collapse transition, which is unusually sharp in Mg 2+ , has the characteristics of a first-order phase transition. Partial digestion with ribonuclease T1 under identical conditions showed that this transition correlated with the assembly of double helices in the ribozyme core. Fivefold higher Mg 2+ concentrations were required for self-splicing, indicating that compaction occurs before native tertiary interactions are fully stabilized. No further decrease in Rg was observed between 1.7 and 20 mM MgCl 2 , indicating that the intermediates have the same dimensions as the native ribozyme, within the uncertainty of the data (± 1 Angstroms). A more gradual transition to a final R g of approximately 33.5 Angstroms was observed between 0.45 and 2 M NaCl. This confirms the expectation that monovalent ions not only are less efficient in charge neutralization but also contract the RNA less efficiently than multivalent ions

New Evidence for a Black Hole in the Compact Binary Cygnus X-3

Science.gov (United States)

Shrader, Chris R.; Titarchuk, Lev; Shaposhnikov, Nikolai

2010-01-01

The bright and highly variable X-ray and radio source known as Cygnus X-3 was among the first X-ray sources discovered, yet it remains in many ways an enigma. Its known to consist of a massive. Wolf-Rayet primary in an extremely tight orbit with a compact object. Yet one of the most basic of pa.ranietern the mass of the compact object - is not known. Nor is it even clear whether its is a neutron star or a black hole. In this Paper we present our analysis of the broad-band high-energy continua covering a substantial range in luminosity and spectral morphology. We apply these results to a recently identified scaling relationship which has been demonstrated to provide reliable estimates of the compact object mass in a number of accretion powered binaries. This analysis leads us to conclude that the compact object in Cygnus X-3 has a mass greater than 4.2 solar mass thus clearly indicative of a black hole and as such resolving a longstanding issue. The full range of uncertainty in our analysis and from using a. range of recently published distance estimates constrains the compact object mass to lie between 4.2 solar mass and 14.4 solar mass. Our favored estimate, based on a 9.0 kpc distance estimate is approx. l0 solar mass, with the. error margin of 3.2 solar masses. This result may thus pose challenges to shared-envelope evolutionary models of compact binaries. as well as establishing Cygnus X-3 as the first confirmed accretion-powered galactic gamma: ray source.

Effects of bedding quality on lying behavior of dairy cows.

Science.gov (United States)

Fregonesi, J A; Veira, D M; von Keyserlingk, M A G; Weary, D M

2007-12-01

Cows prefer to spend more time lying down in free stalls with more bedding, but no research to date has addressed the effects of bedding quality. Bedding in stalls often becomes wet either from exposure to the elements or from feces and urine. The aim of this study was to test the effect of wet bedding on stall preference and use. Four groups of 6 nonlactating Holstein cows were housed in free stalls bedded daily with approximately 0.1 m of fresh sawdust. Following a 5-d adaptation period, each group of cows was tested sequentially with access to stalls with either dry or wet sawdust bedding (86.4 +/- 2.1 vs. 26.5 +/- 2.1% dry matter), each for 2 d. These no-choice phases were followed by a 2-d free-choice phase during which cows had simultaneous access to stalls containing either wet or dry bedding. Stall usage was assessed by using 24-h video recordings scanned at 10-min intervals, and responses were analyzed by using a mixed model, with group (n = 4) as the observational unit. The minimum and maximum environmental temperatures during the experiment were 3.4 +/- 2.2 and 6.8 +/- 2.5 degrees C, respectively. When cows had access only to stalls with wet bedding, they spent 8.8 +/- 0.8 h/d lying down, which increased to 13.8 +/- 0.8 h/d when stalls with dry bedding were provided. Cows spent more time standing with their front 2 hooves in the stall when provided with wet vs. dry bedding (92 +/- 10 vs. 32 +/- 10 min/d). During the free-choice phase, all cows spent more time lying down in the dry stalls, spending 12.5 +/- 0.3 h/d in the dry stalls vs. 0.9 +/- 0.3 h/ d in stalls with wet bedding. In conclusion, dairy cows show a clear preference for a dry lying surface, and they spend much more time standing outside the stall when only wet bedding is available.

Perspectives in Lie theory

CERN Document Server

Carnovale, Giovanna; Caselli, Fabrizio; Concini, Corrado; Sole, Alberto

2017-01-01

Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

Orthogonal expansions related to compact Gelfand pairs

DEFF Research Database (Denmark)

Berg, Christian; Peron, Ana P.; Porcu, Emilio

2017-01-01

. The functions of this class are the functions having a uniformly convergent expansion ∑ϕεZB(ϕ)(u)ϕ(x) for xεG,uεL, where the sum is over the space Z of positive definite spherical functions ϕ:G→C for the Gelfand pair, and (B(ϕ))ϕεZ is a family of continuous positive definite functions on L such that ∑ϕε......For a locally compact group G, let P(G) denote the set of continuous positive definite functions f:G→C. Given a compact Gelfand pair (G,K) and a locally compact group L, we characterize the class PK#(G,L) of functions fεP(G×L) which are bi-invariant in the G-variable with respect to K......(d)) and (U(q),U(q-1)) as well as for the product of these Gelfand pairs.The result generalizes recent theorems of Berg-Porcu (2016) and Guella-Menegatto (2016)....

Sintered nuclear fuel compact and method for its production

International Nuclear Information System (INIS)

Peehs, M.; Dorr, W.

1988-01-01

This patent describes a method of producing a sintered nuclear fuel compact with which reactivity losses in a nuclear reactor having long fuel element cycles are avoided, which comprises, forming a compact of a mixture of powders containing at least one nuclear fuel oxide selected from the group consisting of UO/sub 2/, PuO/sub 2/, ThO/sub 2/, mixed oxide (U, Pu)O/sub 2/ and mixed oxide (U, Th)O/sub 2/, at least one neutron poison selected from the group consisting of UB/sub x/, where x=2; 4 and/or 12 and B/sub 4/C, and sintering the compact of the mixture of powders so that the neutron piston is embedded in a sintered matrix of the nuclear fuel oxide at a treatment temperature in a range from 1000 0 C to 1400 0 C in an oxidizing sintering atmosphere, and then heat treating the sintered compact in a reducing gas atmosphere

Complex quantum groups

International Nuclear Information System (INIS)

Drabant, B.; Schlieker, M.

1993-01-01

The complex quantum groups are constructed. They are q-deformations of the real Lie groups which are obtained as the complex groups corresponding to the Lie algebras of type A n-1 , B n , C n . Following the ideas of Faddeev, Reshetikhin and Takhtajan Hopf algebras of regular functionals U R for these complexified quantum groups are constructed. One has thus in particular found a construction scheme for the q-Lorentz algebra to be identified as U(sl q (2,C). (orig.)

Searching gamma-ray bursts for gravitational lensing echoes - Implications for compact dark matter

Science.gov (United States)

Nemiroff, R. J.; Norris, J. P.; Wickramasinghe, W. A. D. T.; Horack, J. M.; Kouveliotou, C.; Fishman, G. J.; Meegan, C. A.; Wilson, R. B.; Paciesas, W. S.

1993-01-01

The first available 44 gamma-ray bursts (GRBs) detected by the Burst and Transient Source Experiment on board the Compton Gamma-Ray Observatory have been inspected for echo signals following shortly after the main signal. No significant echoes have been found. Echoes would have been expected were the GRBs distant enough and the universe populated with a sufficient density of compact objects composing the dark matter. Constraints on dark matter abundance and GRB redshifts from the present data are presented and discussed. Based on these preliminary results, a universe filled to critical density of compact objects between 10 exp 6.5 and 10 exp 8.1 solar masses are now marginally excluded, or the most likely cosmological distance paradigm for GRBs is not correct. We expect future constraints to be able either to test currently popular cosmological dark matter paradigms or to indicate that GRBs do not lie at cosmological distances.

Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED

International Nuclear Information System (INIS)

Goeckeler, M.; Horsley, R.; Rakow, P.; Schierholz, G.; Sommer, R.

1992-01-01

We investigate the ultra-violet behavior of non-compact lattice QED with light staggered fermions. The main question is whether QED is a non-trivial theory in the continuum limit, and if not, what is its range of validity as a low-energy theory. Perhaps the limited range of validity could offer an explanation of why the fine-structure constant is so small. Non-compact QED undergoes a second-order chiral phase transition at strong coupling, at which the continuum limit can be taken. We examine the phase diagram and the critical behavior of the theory in detail. Moreover, we address the question as to whether QED confines in the chirally broken phase. This is done by investigating the potential between static external charges. We then compute the renormalized charge and derive the Callan-Symanzik β-function in the critical region. No ultra-violet stable zero is found. Instead, we find that the evolution of charge is well described by renormalized perturbation theory, and that the renormalized charge vanishes at the critical point. The consequence is that QED can only be regarded as a cut-off theory. We evaluate the maximum value of the cut-off as a function of the renormalized charge. Next, we compute the masses of fermion-antifermion composite states. The scaling behavior of these masses is well described by an effective action with mean-field critical exponents plus logarithmic corrections. This indicates that also the matter sector of the theory is non-interacting. Finally, we investigate and compare the renormalization group flow of different quantities. Altogether, we find that QED is a valid theory only for samll renormalized charges. (orig.)

Classification of real Lie superalgebras based on a simple Lie algebra, giving rise to interesting examples involving {mathfrak {su}}(2,2)

Science.gov (United States)

Guzzo, H.; Hernández, I.; Sánchez-Valenzuela, O. A.

2014-09-01

Finite dimensional semisimple real Lie superalgebras are described via finite dimensional semisimple complex Lie superalgebras. As an application of these results, finite dimensional real Lie superalgebras mathfrak {m}=mathfrak {m}_0 oplus mathfrak {m}_1 for which mathfrak {m}_0 is a simple Lie algebra are classified up to isomorphism.

The Centroid of a Lie Triple Algebra

Directory of Open Access Journals (Sweden)

Xiaohong Liu

2013-01-01

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

Time-lapse imagery of Adélie penguins reveals differential winter strategies and breeding site occupation

Science.gov (United States)

Southwell, Colin; Emmerson, Louise; Lunn, Daniel

2018-01-01

Polar seabirds adopt different over-wintering strategies to survive and build condition during the critical winter period. Penguin species either reside at the colony during the winter months or migrate long distances. Tracking studies and survey methods have revealed differences in winter migration routes among penguin species and colonies, dependent on both biotic and abiotic factors present. However, scan sampling methods are rarely used to reveal non-breeding behaviors during winter and little is known about presence at the colony site over this period. Here we show that Adélie penguins on the Yalour Islands in the Western Antarctic Peninsula (WAP) are present year-round at the colony and undergo a mid-winter peak in abundance during winter. We found a negative relationship between daylight hours and penguin abundance when either open water or compact ice conditions were present, suggesting that penguins return to the breeding colony when visibility is lowest for at-sea foraging and when either extreme low or high levels of sea ice exist offshore. In contrast, Adélie penguins breeding in East Antarctica were not observed at the colonies during winter, suggesting that Adélie penguins undergo differential winter strategies in the marginal ice zone on the WAP compared to those in East Antarctica. These results demonstrate that cameras can successfully monitor wildlife year-round in areas that are largely inaccessible during winter. PMID:29561876

BTZ black hole from Poisson–Lie T-dualizable sigma models with spectators

Directory of Open Access Journals (Sweden)

A. Eghbali

2017-09-01

Full Text Available The non-Abelian T-dualization of the BTZ black hole is discussed in detail by using the Poisson–Lie T-duality in the presence of spectators. We explicitly construct a dual pair of sigma models related by Poisson–Lie symmetry. The original model is built on a 2+1-dimensional manifold M≈O×G, where G as a two-dimensional real non-Abelian Lie group acts freely on M, while O is the orbit of G in M. The findings of our study show that the original model indeed is canonically equivalent to the SL(2,R Wess–Zumino–Witten (WZW model for a given value of the background parameters. Moreover, by a convenient coordinate transformation we show that this model describes a string propagating in a spacetime with the BTZ black hole metric in such a way that a new family of the solutions to low energy string theory with the BTZ black hole vacuum metric, constant dilaton field and a new torsion potential is found. The dual model is built on a 2+1-dimensional target manifold M˜ with two-dimensional real Abelian Lie group G˜ acting freely on it. We further show that the dual model yields a three-dimensional charged black string for which the mass M and axion charge Q per unit length are calculated. After that, the structure and asymptotic nature of the dual space–time including the horizon and singularity are determined.

Lie n-algebras of BPS charges

Energy Technology Data Exchange (ETDEWEB)

Sati, Hisham [University of Pittsburgh,Pittsburgh, PA, 15260 (United States); Mathematics Program, Division of Science and Mathematics, New York University Abu Dhabi,Saadiyat Island, Abu Dhabi (United Arab Emirates); Schreiber, Urs [Mathematics Institute of the Academy,Žitna 25, Praha 1, 115 67 (Czech Republic)

2017-03-16

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 charges as they are lifted from ordinary cohomology to twisted K-theory. This supports the proposal that M-brane charges live in a twisted cohomology theory.

The group theory of oxidation II: cosets of non-split groups

International Nuclear Information System (INIS)

Keurentjes, Arjan

2003-01-01

The oxidation program given in the first article of this series (see preceding article in this issue) is extended to cover oxidation of 3d sigma model theories on a coset G/H, with G non-compact (but not necessarily split), and H the maximal compact subgroup. We recover the matter content, the equations of motion and Bianchi identities from group lattice and Cartan involution. Satake diagrams provide an elegant tool for the computations, the maximal oxidation dimension, and group disintegration chains can be directly read off. We give a complete list of theories that can be recovered from oxidation of a 3-dimensional coset sigma model on G/H, where G is a simple non-compact group

Two parameters Lie group analysis and numerical solution of unsteady free convective flow of non-Newtonian fluid

Directory of Open Access Journals (Sweden)

M.J. Uddin

2016-09-01

Full Text Available The two-dimensional unsteady laminar free convective heat and mass transfer fluid flow of a non-Newtonian fluid adjacent to a vertical plate has been analyzed numerically. The two parameters Lie group transformation method that transforms the three independent variables into a single variable is used to transform the continuity, the momentum, the energy and the concentration equations into a set of coupled similarity equations. The transformed equations have been solved by the Runge–Kutta–Fehlberg fourth-fifth order numerical method with shooting technique. Numerical calculations were carried out for the various parameters entering into the problem. The dimensionless velocity, temperature and concentration profiles were shown graphically and the skin friction, heat and mass transfer rates were given in tables. It is found that friction factor and heat transfer (mass transfer rate for methanol are higher (lower than those of hydrogen and water vapor. Friction factor decreases while heat and mass transfer rate increase as the Prandtl number increases. Friction (heat and mass transfer rate factor of Newtonian fluid is higher (lower than the dilatant fluid.

Testosterone Administration Reduces Lying in Men

NARCIS (Netherlands)

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

The principle of the indistinguishability of identical particles and the Lie algebraic approach to the field quantisation

International Nuclear Information System (INIS)

Govorkov, A.B.

1980-01-01

The density matrix, rather than the wavefunction describing the system of a fixed number of non-relativistic identical particles, is subject to the second quantisation. Here the bilinear operators which move a particle from a given state to another appear and satisfy the Lie algebraic relations of the unitary group SU(rho) when the dimension rho→infinity. The drawing into consideration of the system with a variable number of particles implies the extension of this algebra into one of the simple Lie algebras of classical (orthogonal, symplectic or unitary) groups in the even-dimensional spaces. These Lie algebras correspond to the para-Fermi-, para-Bose- and para-uniquantisation of fields, respectively. (author)

ULTRAVIOLET+INFRARED STAR FORMATION RATES: HICKSON COMPACT GROUPS WITH SWIFT AND SPITZER

International Nuclear Information System (INIS)

Tzanavaris, P.; Hornschemeier, A. E.; Immler, S.; Gallagher, S. C.; Johnson, K. E.; Reines, A. E.; Gronwall, C.; Hoversten, E.; Charlton, J. C.

2010-01-01

We present Swift UVOT ultraviolet (UV; 1600-3000 A) data with complete three-band UV photometry for a sample of 41 galaxies in 11 nearby ( -1 ) Hickson Compact Groups (HCGs) of galaxies. We use UVOT uvw2-band (2000 A) photometry to estimate the dust-unobscured component, SFR UV , of the total star formation rate, SFR TOTAL . We use Spitzer MIPS 24 μm photometry to estimate SFR IR , the component of SFR TOTAL that suffers dust extinction in the UV and is re-emitted in the IR. By combining the two components, we obtain SFR TOTAL estimates for all HCG galaxies. We obtain total stellar mass, M * , estimates by means of Two Micron All Sky Survey K s -band luminosities, and use them to calculate specific star formation rates, SSFR ≡ SFR TOTAL /M * . SSFR values show a clear and significant bimodality, with a gap between low (∼ -11 yr -1 ) and high-SSFR (∼>1.2 x 10 -10 yr -1 ) systems. We compare this bimodality to the previously discovered bimodality in α IRAC , the MIR activity index from a power-law fit to the Spitzer IRAC 4.5-8 μm data for these galaxies. We find that all galaxies with α IRAC ≤ 0 ( >0) are in the high- (low-) SSFR locus, as expected if high levels of star-forming activity power MIR emission from polycyclic aromatic hydrocarbon molecules and a hot dust continuum. Consistent with this finding, all elliptical/S0 galaxies are in the low-SSFR locus, while 22 out of 24 spirals/irregulars are in the high-SSFR locus, with two borderline cases. We further divide our sample into three subsamples (I, II, and III) according to decreasing H I richness of the parent galaxy group to which a galaxy belongs. Consistent with the SSFR and α IRAC bimodality, 12 out of 15 type I (11 out of 12 type III) galaxies are in the high- (low-) SSFR locus, while type II galaxies span almost the full range of SSFR values. We use the Spitzer Infrared Nearby Galaxy Survey (SINGS) to construct a comparison subsample of galaxies that (1) match HCG galaxies in J-band total

The Effect of Telling Lies on Belief in the Truth

Directory of Open Access Journals (Sweden)

Danielle Polage

2017-11-01

Full Text Available The current study looks at the effect of telling lies, in contrast to simply planning lies, on participants’ belief in the truth. Participants planned and told a lie, planned to tell a lie but didn’t tell it, told an unplanned lie, or neither planned nor told a lie (control about events that did not actually happen to them. Participants attempted to convince researchers that all of the stories told were true. Results show that telling a lie plays a more important role in inflating belief scores than simply preparing the script of a lie. Cognitive dissonance may lead to motivated forgetting of information that does not align with the lie. This research suggests that telling lies may lead to confusion as to the veracity of the lie leading to inflated belief scores.

Polyakov-Wiegmann formula and multiplicative gerbes

International Nuclear Information System (INIS)

Gawedzki, Krzysztof; Waldorf, Konrad

2009-01-01

An unambiguous definition of Feynman amplitudes in the Wess-Zumino-Witten sigma model and the Chern-Simon gauge theory with a general Lie group is determined by a certain geometric structure on the group. For the WZW amplitudes, this is a (bundle) gerbe with connection of an appropriate curvature whereas for the CS amplitudes, the gerbe has to be additionally equipped with a multiplicative structure assuring its compatibility with the group multiplication. We show that for simple compact Lie groups the obstruction to the existence of a multiplicative structure is provided by a 2-cocycle of phases that appears in the Polyakov-Wiegmann formula relating the Wess-Zumino action functional of the product of group-valued fields to the sum of the individual contributions. These phases were computed long time ago for all compact simple Lie groups. If they are trivial, then the multiplicative structure exists and is unique up to isomorphism.

Short communication: Association of lying behavior and subclinical ketosis in transition dairy cows.

Science.gov (United States)

Kaufman, E I; LeBlanc, S J; McBride, B W; Duffield, T F; DeVries, T J

2016-09-01

The objective of this study was to characterize the association of lying behavior and subclinical ketosis (SCK) in transition dairy cows. A total of 339 dairy cows (107 primiparous and 232 multiparous) on 4 commercial dairy farms were monitored for lying behavior and SCK from 14d before calving until 28 d after calving. Lying time, frequency of lying bouts, and average lying bout length were measured using automated data loggers 24h/d. Cows were tested for SCK 1×/wk by taking a blood sample and analyzing for β-hydroxybutyrate; cows with β-hydroxybutyrate ≥1.2mmol/L postpartum were considered to have SCK. Cases of retained placenta, metritis, milk fever, or mastitis during the study period were recorded and cows were categorized into 1 of 4 groups: healthy (HLT) cows had no SCK or any other health problem (n=139); cows treated for at least 1 health issue other than SCK (n=50); SCK (HYK) cows with no other health problems during transition (n=97); or subclinically ketotic plus (HYK+) cows that had SCK and 1 or more other health problems (n=53). Daily lying time was summarized by week and comparisons were made between HLT, HYK, and HYK+, respectively. We found no difference among health categories in lying time, bout frequency, or bout length fromwk -2 towk +4 relative to calving for first-lactation cows. Differences in lying time for multiparous cows were seen inwk +1, when HYK+ cows spent 92±24.0 min/d more time lying down than HLT cows, and duringwk +3 and +4 when HYK cows spent 44±16.7 and 41±18.9 min/d, respectively, more time lying down than HLT cows. Increased odds of HYK+ were found to be associated with higher parity, longer dry period, and greater stall stocking density inwk -1 and longer lying time duringwk +1. When comparing HYK to HLT cows, the same variables were associated with odds of SCK; however, lying time was not retained in the final model. These results suggest that monitoring lying time may contribute to identifying multiparous cows

Biderivations of finite dimensional complex simple Lie algebras

OpenAIRE

Tang, Xiaomin

2016-01-01

In this paper, we prove that a biderivation of a finite dimensional complex simple Lie algebra without the restriction of skewsymmetric is inner. As an application, the biderivation of a general linear Lie algebra is presented. In particular, we find a class of a non-inner and non-skewsymmetric biderivations. Furthermore, we also get the forms of linear commuting maps on the finite dimensional complex simple Lie algebra or general linear Lie algebra.

Mouse Embryo Compaction.

Science.gov (United States)

White, M D; Bissiere, S; Alvarez, Y D; Plachta, N

2016-01-01

Compaction is a critical first morphological event in the preimplantation development of the mammalian embryo. Characterized by the transformation of the embryo from a loose cluster of spherical cells into a tightly packed mass, compaction is a key step in the establishment of the first tissue-like structures of the embryo. Although early investigation of the mechanisms driving compaction implicated changes in cell-cell adhesion, recent work has identified essential roles for cortical tension and a compaction-specific class of filopodia. During the transition from 8 to 16 cells, as the embryo is compacting, it must also make fundamental decisions regarding cell position, polarity, and fate. Understanding how these and other processes are integrated with compaction requires further investigation. Emerging imaging-based techniques that enable quantitative analysis from the level of cell-cell interactions down to the level of individual regulatory molecules will provide a greater understanding of how compaction shapes the early mammalian embryo. © 2016 Elsevier Inc. All rights reserved.

On numerical characteristics of subvarieties for three varieties of Lie algebras

International Nuclear Information System (INIS)

Petrogradskii, V M

1999-01-01

Let V be a variety of Lie algebras. For each n we consider the dimension of the space of multilinear elements in n distinct letters of a free algebra of this variety. This gives rise to the codimension sequence c n (V). To study the exponential growth one defines the exponent of the variety. The variety of Lie algebras with nilpotent derived subalgebra N s A is known to have Exp(N s A)=s. Over a field of characteristic zero the exponent of every subvariety V subset of N s A is known to be an integer. We shall prove that this is true over any field. Unlike associative algebras, for varieties of Lie algebras it is typical to have superexponential growth for the codimension sequence. Earlier the author introduced a scale for measuring this growth. The following extreme property is established for two varieties AN 2 and A 3 . Any subvariety in each of them cannot be 'just slightly smaller' in terms of this scale. That is, either a subvariety lies at the same point of the scale as the variety itself, or it is situated substantially lower on the scale. These results are also established over an arbitrary field and without using the representation theory of symmetric groups

White Lies in Hand: Are Other-Oriented Lies Modified by Hand Gestures? Possibly Not.

Science.gov (United States)

Cantarero, Katarzyna; Parzuchowski, Michal; Dukala, Karolina

2017-01-01

Previous studies have shown that the hand-over-heart gesture is related to being more honest as opposed to using self-centered dishonesty. We assumed that the hand-over-heart gesture would also relate to other-oriented dishonesty, though the latter differs highly from self-centered lying. In Study 1 ( N = 79), we showed that performing a hand-over-heart gesture diminished the tendency to use other-oriented white lies and that the fingers crossed behind one's back gesture was not related to higher dishonesty. We then pre-registered and conducted Study 2 ( N = 88), which was designed following higher methodological standards than Study 1. Contrary, to the findings of Study 1, we found that using the hand-over-heart gesture did not result in refraining from using other-oriented white lies. We discuss the findings of this failed replication indicating the importance of strict methodological guidelines in conducting research and also reflect on relatively small effect sizes related to some findings in embodied cognition.

WITNESSING GAS MIXING IN THE METAL DISTRIBUTION OF THE HICKSON COMPACT GROUP HCG 31

International Nuclear Information System (INIS)

Torres-Flores, S.; Alfaro-Cuello, M.; De Oliveira, C. Mendes; Amram, P.; Carrasco, E. R.; De Mello, D. F.

2015-01-01

We present for the first time direct evidence that in a merger of disk galaxies, the pre-existing central metallicities will mix as a result of gas being transported in the merger interface region along the line that joins the two coalescing nuclei. This is shown using detailed two-dimensional kinematics as well as metallicity measurements for the nearby ongoing merger in the center of the compact group HCG 31. We focus on the emission line gas, which is extensive in the system. The two coalescing cores display similar oxygen abundances. While in between the two nuclei, the metallicity changes smoothly from one nucleus to the other indicating a mix of metals in this region, which is confirmed by the high-resolution Hα kinematics (R = 45,900). This nearby system is especially important because it involves the merging of two fairly low-mass and clumpy galaxies (LMC-like galaxies), making it an important system for comparison with high-redshift galaxies

WITNESSING GAS MIXING IN THE METAL DISTRIBUTION OF THE HICKSON COMPACT GROUP HCG 31

Energy Technology Data Exchange (ETDEWEB)

Torres-Flores, S.; Alfaro-Cuello, M. [Departamento de Física, Universidad de La Serena, Av. Cisternas 1200, La Serena (Chile); De Oliveira, C. Mendes [Instituto de Astronomia, Geofísica e Ciências Atmosféricas da Universidade de São Paulo, Cidade Universitária, CEP:05508-900, São Paulo, SP (Brazil); Amram, P. [Aix Marseille Université, CNRS, LAM (Laboratoire d' Astrophysique de Marseille) UMR 7326, F-13388, Marseille (France); Carrasco, E. R. [Gemini Observatory/AURA, Southern Operations Center, Casilla 603, La Serena (Chile); De Mello, D. F., E-mail: storres@dfuls.cl [Catholic University of America, Washington, DC 20064 (United States)

2015-01-01

We present for the first time direct evidence that in a merger of disk galaxies, the pre-existing central metallicities will mix as a result of gas being transported in the merger interface region along the line that joins the two coalescing nuclei. This is shown using detailed two-dimensional kinematics as well as metallicity measurements for the nearby ongoing merger in the center of the compact group HCG 31. We focus on the emission line gas, which is extensive in the system. The two coalescing cores display similar oxygen abundances. While in between the two nuclei, the metallicity changes smoothly from one nucleus to the other indicating a mix of metals in this region, which is confirmed by the high-resolution Hα kinematics (R = 45,900). This nearby system is especially important because it involves the merging of two fairly low-mass and clumpy galaxies (LMC-like galaxies), making it an important system for comparison with high-redshift galaxies.

A new approach for categorizing pig lying behaviour based on a Delaunay triangulation method.

Science.gov (United States)

Nasirahmadi, A; Hensel, O; Edwards, S A; Sturm, B

2017-01-01

Machine vision-based monitoring of pig lying behaviour is a fast and non-intrusive approach that could be used to improve animal health and welfare. Four pens with 22 pigs in each were selected at a commercial pig farm and monitored for 15 days using top view cameras. Three thermal categories were selected relative to room setpoint temperature. An image processing technique based on Delaunay triangulation (DT) was utilized. Different lying patterns (close, normal and far) were defined regarding the perimeter of each DT triangle and the percentages of each lying pattern were obtained in each thermal category. A method using a multilayer perceptron (MLP) neural network, to automatically classify group lying behaviour of pigs into three thermal categories, was developed and tested for its feasibility. The DT features (mean value of perimeters, maximum and minimum length of sides of triangles) were calculated as inputs for the MLP classifier. The network was trained, validated and tested and the results revealed that MLP could classify lying features into the three thermal categories with high overall accuracy (95.6%). The technique indicates that a combination of image processing, MLP classification and mathematical modelling can be used as a precise method for quantifying pig lying behaviour in welfare investigations.

3-Lie bialgebras (Lb,Cd and (Lb,Ce

Directory of Open Access Journals (Sweden)

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.

Using Lie Symmetry Analysis to Solve a Problem That Models Mass Transfer from a Horizontal Flat Plate

Directory of Open Access Journals (Sweden)

W. Sinkala

2012-01-01

Full Text Available We use Lie symmetry analysis to solve a boundary value problem that arises in chemical engineering, namely, mass transfer during the contact of a solid slab with an overhead flowing fluid. This problem was earlier tackled using Adomian decomposition method (Fatoorehchi and Abolghasemi 2011, leading to the Adomian series form of solution. It turns out that the application of Lie group analysis yields an elegant form of the solution. After introducing the governing mathematical model and some preliminaries of Lie symmetry analysis, we compute the Lie point symmetries admitted by the governing equation and use these to construct the desired solution as an invariant solution.

Quaternionic and Poisson-Lie structures in three-dimensional gravity: The cosmological constant as deformation parameter

International Nuclear Information System (INIS)

Meusburger, C.; Schroers, B. J.

2008-01-01

Each of the local isometry groups arising in three-dimensional (3d) gravity can be viewed as a group of unit (split) quaternions over a ring which depends on the cosmological constant. In this paper we explain and prove this statement and use it as a unifying framework for studying Poisson structures associated with the local isometry groups. We show that, in all cases except for the case of Euclidean signature with positive cosmological constant, the local isometry groups are equipped with the Poisson-Lie structure of a classical double. We calculate the dressing action of the factor groups on each other and find, among others, a simple and unified description of the symplectic leaves of SU(2) and SL(2,R). We also compute the Poisson structure on the dual Poisson-Lie groups of the local isometry groups and on their Heisenberg doubles; together, they determine the Poisson structure of the phase space of 3d gravity in the so-called combinatorial description

Internally connected graphs and the Kashiwara-Vergne Lie algebra

Science.gov (United States)

Felder, Matteo

2018-02-01

It is conjectured that the Kashiwara-Vergne Lie algebra \\widehat{krv}_2 is isomorphic to the direct sum of the Grothendieck-Teichmüller Lie algebra grt_1 and a one-dimensional Lie algebra. In this paper, we use the graph complex of internally connected graphs to define a nested sequence of Lie subalgebras of \\widehat{krv}_2 whose intersection is grt_1 , thus giving a way to interpolate between these two Lie algebras.

Lie-Algebras. Pt. 1

International Nuclear Information System (INIS)

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

1990-01-01

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

Oxytocin promotes group-serving dishonesty.

Science.gov (United States)

Shalvi, Shaul; De Dreu, Carsten K W

2014-04-15

To protect and promote the well-being of others, humans may bend the truth and behave unethically. Here we link such tendencies to oxytocin, a neuropeptide known to promote affiliation and cooperation with others. Using a simple coin-toss prediction task in which participants could dishonestly report their performance levels to benefit their group's outcome, we tested the prediction that oxytocin increases group-serving dishonesty. A double-blind, placebo-controlled experiment allowing individuals to lie privately and anonymously to benefit themselves and fellow group members showed that healthy males (n = 60) receiving intranasal oxytocin, rather than placebo, lied more to benefit their group, and did so faster, yet did not necessarily do so because they expected reciprocal dishonesty from fellow group members. Treatment effects emerged when lying had financial consequences and money could be gained; when losses were at stake, individuals in placebo and oxytocin conditions lied to similar degrees. In a control condition (n = 60) in which dishonesty only benefited participants themselves, but not fellow group members, oxytocin did not influence lying. Together, these findings fit a functional perspective on morality revealing dishonesty to be plastic and rooted in evolved neurobiological circuitries, and align with work showing that oxytocin shifts the decision-maker's focus from self to group interests. These findings highlight the role of bonding and cooperation in shaping dishonesty, providing insight into when and why collaboration turns into corruption.

Preschoolers' Understanding of Lies and Innocent and Negligent Mistakes.

Science.gov (United States)

Siegal, Michael; Peterson, Candida C.

1998-01-01

Examined preschoolers' ability to distinguish innocent and negligent mistakes from lies. Found that, when asked to identify a mistake or lie about a food's contact with contaminants and identify a bystander's reaction, children distinguished mistakes from lies; they could also discriminate between lies and both negligent mistakes that generate…

Internally connected graphs and the Kashiwara-Vergne Lie algebra

OpenAIRE

Felder, Matteo

2016-01-01

It is conjectured that the Kashiwara-Vergne Lie algebra $\\widehat{\\mathfrak{krv}}_2$ is isomorphic to the direct sum of the Grothendieck-Teichm\\"uller Lie algebra $\\mathfrak{grt}_1$ and a one-dimensional Lie algebra. In this paper, we use the graph complex of internally connected graphs to define a nested sequence of Lie subalgebras of $\\widehat{\\mathfrak{krv}}_2$ whose intersection is $\\mathfrak{grt}_1$, thus giving a way to interpolate between these two Lie algebras.

Should non-disclosures be considered as morally equivalent to lies within the doctor-patient relationship?

Science.gov (United States)

Cox, Caitriona L; Fritz, Zoe

2016-10-01

In modern practice, doctors who outright lie to their patients are often condemned, yet those who employ non-lying deceptions tend to be judged less critically. Some areas of non-disclosure have recently been challenged: not telling patients about resuscitation decisions; inadequately informing patients about risks of alternative procedures and withholding information about medical errors. Despite this, there remain many areas of clinical practice where non-disclosures of information are accepted, where lies about such information would not be. Using illustrative hypothetical situations, all based on common clinical practice, we explore the extent to which we should consider other deceptive practices in medicine to be morally equivalent to lying. We suggest that there is no significant moral difference between lying to a patient and intentionally withholding relevant information: non-disclosures could be subjected to Bok's 'Test of Publicity' to assess permissibility in the same way that lies are. The moral equivalence of lying and relevant non-disclosure is particularly compelling when the agent's motivations, and the consequences of the actions (from the patient's perspectives), are the same. We conclude that it is arbitrary to claim that there is anything inherently worse about lying to a patient to mislead them than intentionally deceiving them using other methods, such as euphemism or non-disclosure. We should question our intuition that non-lying deceptive practices in clinical practice are more permissible and should thus subject non-disclosures to the same scrutiny we afford to lies. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

Legitimate lies : The relationship between omission, commission, and cheating

NARCIS (Netherlands)

Pittarello, Andrea; Rubaltelli, Enrico; Motro, Daphna

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

The fate of high redshift massive compact galaxies in dense environments

Energy Technology Data Exchange (ETDEWEB)

Kaufmann, Tobias; /Zurich, ETH; Mayer, Lucio; /Zurich U.; Carollo, Marcella; /Zurich, ETH; Feldmann, Robert; /Fermilab /Chicago U., KICP

2012-01-01

Massive compact galaxies seem to be more common at high redshift than in the local universe, especially in denser environments. To investigate the fate of such massive galaxies identified at z {approx} 2 we analyse the evolution of their properties in three cosmological hydrodynamical simulations that form virialized galaxy groups of mass {approx} 10{sup 13} M{sub {circle_dot}} hosting a central massive elliptical/S0 galaxy by redshift zero. We find that at redshift {approx} 2 the population of galaxies with M{sub *} > 2 x 10{sup 10} M{sub {circle_dot}} is diverse in terms of mass, velocity dispersion, star formation and effective radius, containing both very compact and relatively extended objects. In each simulation all the compact satellite galaxies have merged into the central galaxy by redshift 0 (with the exception of one simulation where one of such satellite galaxy survives). Satellites of similar mass at z = 0 are all less compact than their high redshift counterparts. They form later than the galaxies in the z = 2 sample and enter the group potential at z < 1, when dynamical friction times are longer than the Hubble time. Also, by z = 0 the central galaxies have increased substantially their characteristic radius via a combination of in situ star formation and mergers. Hence in a group environment descendants of compact galaxies either evolve towards larger sizes or they disappear before the present time as a result of the environment in which they evolve. Since the group-sized halos that we consider are representative of dense environments in the {Lambda}CDM cosmology, we conclude that the majority of high redshift compact massive galaxies do not survive until today as a result of the environment.

Ombud’s Corner: a world without lies?

CERN Multimedia

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...

Cartan calculus on quantum Lie algebras

International Nuclear Information System (INIS)

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

1993-01-01

A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions au into one big algebra, the ''Cartan Calculus.''

Low-dimensional filiform Lie algebras over finite fields

OpenAIRE

Falcón Ganfornina, Óscar Jesús; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vasek, Vladimir (Coordinador); Shmaliy, Yuriy S. (Coordinador); Trcek, Denis (Coordinador); Kobayashi, Nobuhiko P. (Coordinador); Choras, Ryszard S. (Coordinador); Klos, Zbigniew (Coordinador)

2011-01-01

In this paper we use some objects of Graph Theory to classify low-dimensional filiform Lie algebras over finite fields. The idea lies in the representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As results, which can be applied in several branches of Physics or Engineering, for instance, we find out that there exist, up to isomorphism, six 6-dimensional filiform Lie algebras over Z/pZ, for p = 2, 3, 5. Pl...

Expansion of the Lie algebra and its applications

International Nuclear Information System (INIS)

Guo Fukui; Zhang Yufeng

2006-01-01

We take the Lie algebra A1 as an example to illustrate a detail approach for expanding a finite dimensional Lie algebra into a higher-dimensional one. By making use of the late and its resulting loop algebra, a few linear isospectral problems with multi-component potential functions are established. It follows from them that some new integrable hierarchies of soliton equations are worked out. In addition, various Lie algebras may be constructed for which the integrable couplings of soliton equations are obtained by employing the expanding technique of the the Lie algebras

White Lies in Hand: Are Other-Oriented Lies Modified by Hand Gestures? Possibly Not

Directory of Open Access Journals (Sweden)

Katarzyna Cantarero

2017-06-01

Full Text Available Previous studies have shown that the hand-over-heart gesture is related to being more honest as opposed to using self-centered dishonesty. We assumed that the hand-over-heart gesture would also relate to other-oriented dishonesty, though the latter differs highly from self-centered lying. In Study 1 (N = 79, we showed that performing a hand-over-heart gesture diminished the tendency to use other-oriented white lies and that the fingers crossed behind one’s back gesture was not related to higher dishonesty. We then pre-registered and conducted Study 2 (N = 88, which was designed following higher methodological standards than Study 1. Contrary, to the findings of Study 1, we found that using the hand-over-heart gesture did not result in refraining from using other-oriented white lies. We discuss the findings of this failed replication indicating the importance of strict methodological guidelines in conducting research and also reflect on relatively small effect sizes related to some findings in embodied cognition.

On an infinite-dimensional Lie algebra of Virasoro-type

International Nuclear Information System (INIS)

Pei Yufeng; Bai Chengming

2012-01-01

In this paper, we study an infinite-dimensional Lie algebra of Virasoro-type which is realized as an affinization of a two-dimensional Novikov algebra. It is a special deformation of the Lie algebra of differential operators on a circle of order at most 1. There is an explicit construction of a vertex algebra associated with the Lie algebra. We determine all derivations of this Lie algebra in terms of some derivations and centroids of the corresponding Novikov algebra. The universal central extension of this Lie algebra is also determined. (paper)

Infinite-dimensional Lie algebras in 4D conformal quantum field theory

International Nuclear Information System (INIS)

Bakalov, Bojko; Nikolov, Nikolay M; Rehren, Karl-Henning; Todorov, Ivan

2008-01-01

The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of two-dimensional chiral conformal field theory, to a higher (even) dimensional spacetime. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, V M (x, y), where the M span a finite dimensional real matrix algebra M closed under transposition. The associative algebra M is irreducible iff its commutant M' coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite-dimensional Lie algebra: a central extension of sp(∞,R) corresponding to the field R of reals, of u(∞, ∞) associated with the field C of complex numbers, and of so*(4∞) related to the algebra H of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N) and U(N,H)=Sp(2N), respectively

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

International Nuclear Information System (INIS)

Ammar, F; Makhlouf, A; Silvestrov, S

2010-01-01

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

Quartic trace identity for exceptional Lie algebras

International Nuclear Information System (INIS)

Okubo, S.

1979-01-01

Let X be a representation matrix of generic element x of a simple Lie algebra in generic irreducible representation ]lambda] of the Lie algebra. Then, for all exceptional Lie algebras as well as A 1 and A 2 , we can prove the validity of a quartic trace identity Tr(X 4 ) =K (lambda)[Tr(X 2 )] 2 , where the constant K (lambda) depends only upon the irreducible representation ]lambda], and its explicit form is calculated. Some applications of second and fourth order indices have also been discussed

Compact Polarimetry Potentials

Science.gov (United States)

Truong-Loi, My-Linh; Dubois-Fernandez, Pascale; Pottier, Eric

2011-01-01

The goal of this study is to show the potential of a compact-pol SAR system for vegetation applications. Compact-pol concept has been suggested to minimize the system design while maximize the information and is declined as the ?/4, ?/2 and hybrid modes. In this paper, the applications such as biomass and vegetation height estimates are first presented, then, the equivalence between compact-pol data simulated from full-pol data and compact-pol data processed from raw data as such is shown. Finally, a calibration procedure using external targets is proposed.

Compact Dual-Band Zeroth-Order Resonance Antenna

International Nuclear Information System (INIS)

Xu He-Xiu; Wang Guang-Ming; Gong Jian-Qiang

2012-01-01

A novel microstrip zeroth-order resonator (ZOR) antenna and its equivalent circuit model are exploited with two zeroth-order resonances. It is constructed based on a resonant-type composite right/left handed transmission line (CRLH TL) using a Wunderlich-shaped extended complementary single split ring resonator pair (W-ECSSRRP) and a series capacitive gap. The gap either can be utilized for double negative (DNG) ZOR antenna or be removed to engineer a simplified elision-negative ZOR (ENG) antenna. For verification, a DNG ZOR antenna sample is fabricated and measured. Numerical and experimental results agree well with each other, indicating that the omnidirectional radiations occur at two frequency bands which are accounted for by two shunt branches in the circuit model. The size of the antenna is 49% more compact than its previous counterpart. The superiority of W-ECSSRRP over CSSRRP lies in the lower fundamental resonance of the antenna by 38.2% and the introduction of a higher zeroth-order resonance. (fundamental areas of phenomenology(including applications))

Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities

International Nuclear Information System (INIS)

Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.

2007-01-01

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves

Closure of the gauge algebra, generalized Lie equations and Feynman rules

International Nuclear Information System (INIS)

Batalin, I.A.

1984-01-01

A method is given by which an open gauge algebra can always be closed and even made abelian. As a preliminary the generalized Lie equations for the open group are obtained. The Feynman rules for gauge theories with open algebras are derived by reducing the gauge theory to a non-gauge one. (orig.)

Lie n-derivations on 7 -subspace lattice algebras

Indian Academy of Sciences (India)

all x ∈ K and all A ∈ Alg L. Based on this result, a complete characterization of linear n-Lie derivations on Alg L is obtained. Keywords. J -subspace lattice algebras; Lie derivations; Lie n-derivations; derivations. 2010 Mathematics Subject Classification. 47B47, 47L35. 1. Introduction. Let A be an algebra. Recall that a linear ...

Poisson-Lie T-plurality

International Nuclear Information System (INIS)

Unge, Rikard von

2002-01-01

We extend the path-integral formalism for Poisson-Lie T-duality to include the case of Drinfeld doubles which can be decomposed into bi-algebras in more than one way. We give the correct shift of the dilaton, correcting a mistake in the literature. We then use the fact that the six dimensional Drinfeld doubles have been classified to write down all possible conformal Poisson-Lie T-duals of three dimensional space times and we explicitly work out two duals to the constant dilaton and zero anti-symmetric tensor Bianchi type V space time and show that they satisfy the string equations of motion. This space-time was previously thought to have no duals because of the tracefulness of the structure constants. (author)

Compaction of FGD-gypsum

NARCIS (Netherlands)

Stoop, B.T.J.; Larbi, J.A.; Heijnen, W.M.M.

1996-01-01

It is shown that it is possible to produce compacted gypsum with a low porosity and a high strength on a laboratory scale by uniaxial compaction of flue gas desulphurization (FGD-) gypsum powder. Compacted FGD-gypsum cylinders were produced at a compaction pres-sure between 50 and 500 MPa yielding

(U) Influence of Compaction Model Form on Planar and Cylindrical Compaction Geometries

Energy Technology Data Exchange (ETDEWEB)

Fredenburg, David A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Carney, Theodore Clayton [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Fichtl, Christopher Allen [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2018-01-05

The dynamic compaction response of CeO₂ is examined within the frameworks of the Ramp and P-a compaction models. Hydrocode calculations simulating the dynamic response of CeO₂ at several distinct pressures within the compaction region are investigated in both planar and cylindrically convergent geometries. Findings suggest additional validation of the compaction models is warranted under complex loading configurations.

On the exceptional generalised Lie derivative for d≥7

International Nuclear Information System (INIS)

Rosabal, J.A.

2015-01-01

In this work we revisit the E_8×ℝ"+ generalised Lie derivative encoding the algebra of diffeomorphisms and gauge transformations of compactifications of M-theory on eight-dimensional manifolds, by extending certain features of the E_7×ℝ"+ one. Compared to its E_d×ℝ"+, d≤7 counterparts, a new term is needed for consistency. However, we find that no compensating parameters need to be introduced, but rather that the new term can be written in terms of the ordinary generalised gauge parameters by means of a connection. This implies that no further degrees of freedom, beyond those of the field content of the E_8 group, are needed to have a well defined theory. We discuss the implications of the structure of the E_8×ℝ"+ generalised transformation on the construction of the d=8 generalised geometry. Finally, we suggest how to lift the generalised Lie derivative to eleven dimensions.

Normalization in Lie algebras via mould calculus and applications

Science.gov (United States)

Paul, Thierry; Sauzin, David

2017-11-01

We establish Écalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to reduce the Lie-theoretic problem to a mould equation, the solutions of which are remarkably explicit and can be fully described by means of a gauge transformation group. The dynamical applications include the construction of Poincaré-Dulac formal normal forms for a vector field around an equilibrium point, a formal infinite-order multiphase averaging procedure for vector fields with fast angular variables (Hamiltonian or not), or the construction of Birkhoff normal forms both in classical and quantum situations. As a by-product we obtain, in the case of harmonic oscillators, the convergence of the quantum Birkhoff form to the classical one, without any Diophantine hypothesis on the frequencies of the unperturbed Hamiltonians.

A survey on stability and rigidity results for Lie algebras

NARCIS (Netherlands)

Crainic, Marius; Schätz, Florian; Struchiner, Ivan

2014-01-01

We give simple and unified proofs of the known stability and rigidity results for Lie algebras, Lie subalgebras and Lie algebra homomorphisms. Moreover, we investigate when a Lie algebra homomorphism is stable under all automorphisms of the codomain (including outer automorphisms).

Representations of Lie algebras and partial differential equations

CERN Document Server

Xu, Xiaoping

2017-01-01

This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author’s works and his joint works with his former students.  Further, it presents various oscillator generalizations of the classical representation theorem on harmonic polynomials, and highlights new functors from the representation category of a simple Lie algebra to that of another simple Lie algebra. Partial differential equations play a key role in solving certain representation problems. The weight matrices of the minimal and adjoint representations over the simple Lie algebras of types E and F are proved to generate ternary orthogonal linear codes with large minimal distances. New multi-variable hypergeometric functions related to the root systems of simple Lie algebras are introduced in connection with quantum many-body systems in one dimension. In addition, the book identifies certai...

A new class of infinite-dimensional Lie algebras: an analytical continuation of the arbitrary finite-dimensional semisimple Lie algebra

International Nuclear Information System (INIS)

Fradkin, E.S.; Linetsky, V.Ya.

1990-06-01

With any semisimple Lie algebra g we associate an infinite-dimensional Lie algebra AC(g) which is an analytic continuation of g from its root system to its root lattice. The manifest expressions for the structure constants of analytic continuations of the symplectic Lie algebras sp2 n are obtained by Poisson-bracket realizations method and AC(g) for g=sl n and so n are discussed. The representations, central extension, supersymmetric and higher spin generalizations are considered. The Virasoro theory is a particular case when g=sp 2 . (author). 9 refs

Lie transforms and their use in Hamiltonian perturbation theory

International Nuclear Information System (INIS)

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

On the subgroups of PR groups

International Nuclear Information System (INIS)

Lebedenko, V.M.

1979-01-01

The subgroups of PR-groups are being studied, i.e., the subgroups of connected and simply connected nonabelian Lie groups, their Lie algebras being defined by the commuting relations of the type [Hsub(i), Hsub(j)] = rsub(ij)Hsub(i) (i 1 of PR-group G there exists such complementary subgroup G 2 and that group G is expanded in semidirect product G = G 1 xG 2 [ru

A comparison of UVb compact lamps in enabling cutaneous vitamin D synthesis in growing bearded dragons

NARCIS (Netherlands)

Diehl, J J E; Baines, F M; Heijboer, A C; van Leeuwen, J P; Kik, M; Hendriks, W H; Oonincx, D G A B

The effect of exposure to different UVb compact lamps on the vitamin D status of growing bearded dragons (Pogona vitticeps) was studied. Forty-two newly hatched bearded dragons (<24 h old) were allocated to six treatment groups (n = 7 per group). Five groups were exposed to different UVb compact

Everybody else is doing it: exploring social transmission of lying behavior.

Directory of Open Access Journals (Sweden)

Heather Mann

Full Text Available Lying is a common occurrence in social interactions, but what predicts whether an individual will tell a lie? While previous studies have focused on personality factors, here we asked whether lying tendencies might be transmitted through social networks. Using an international sample of 1,687 socially connected pairs, we investigated whether lying tendencies were related in socially connected individuals, and tested two moderators of observed relationships. Participants recruited through a massive open online course reported how likely they would be to engage in specific lies; a friend or relative responded to the same scenarios independently. We classified lies according to their beneficiary (antisocial vs. prosocial lies, and their directness (lies of commission vs. omission, resulting in four unique lying categories. Regression analyses showed that antisocial commission, antisocial omission, and prosocial commission lying tendencies were all uniquely related in connected pairs, even when the analyses were limited to pairs that were not biologically related. For antisocial lies of commission, these relationships were strongest, and were moderated by amount of time spent together. Randomly paired individuals from the same countries were also related in their antisocial commission lying tendencies, signifying country-level norms. Our results indicate that a person's lying tendencies can be predicted by the lying tendencies of his or her friends and family members.

Everybody Else Is Doing It: Exploring Social Transmission of Lying Behavior

Science.gov (United States)

Mann, Heather; Garcia-Rada, Ximena; Houser, Daniel; Ariely, Dan

2014-01-01

Lying is a common occurrence in social interactions, but what predicts whether an individual will tell a lie? While previous studies have focused on personality factors, here we asked whether lying tendencies might be transmitted through social networks. Using an international sample of 1,687 socially connected pairs, we investigated whether lying tendencies were related in socially connected individuals, and tested two moderators of observed relationships. Participants recruited through a massive open online course reported how likely they would be to engage in specific lies; a friend or relative responded to the same scenarios independently. We classified lies according to their beneficiary (antisocial vs. prosocial lies), and their directness (lies of commission vs. omission), resulting in four unique lying categories. Regression analyses showed that antisocial commission, antisocial omission, and prosocial commission lying tendencies were all uniquely related in connected pairs, even when the analyses were limited to pairs that were not biologically related. For antisocial lies of commission, these relationships were strongest, and were moderated by amount of time spent together. Randomly paired individuals from the same countries were also related in their antisocial commission lying tendencies, signifying country-level norms. Our results indicate that a person's lying tendencies can be predicted by the lying tendencies of his or her friends and family members. PMID:25333483

Canonical realizations of the Lie algebra sp(2n,R)

International Nuclear Information System (INIS)

Havlicek, M.; Lassner, W.

1975-01-01

The generators of the Lie algebra of the symplectic group sp(2n,R) are, rezcurently, realied by means of polynomials in the quantum canonical variables qsub(i) and psub(i), i=1,...,d(2n-d);d=1,...,n. These realisations are skew-hermitean, the Casimir operators are realised by constant multiples of identity element and they depend on d free real parameters

Earthquakes - a danger to deep-lying repositories?

International Nuclear Information System (INIS)

2012-03-01

This booklet issued by the Swiss National Cooperative for the Disposal of Radioactive Waste NAGRA takes a look at geological factors concerning earthquakes and the safety of deep-lying repositories for nuclear waste. The geological processes involved in the occurrence of earthquakes are briefly looked at and the definitions for magnitude and intensity of earthquakes are discussed. Examples of damage caused by earthquakes are given. The earthquake situation in Switzerland is looked at and the effects of earthquakes on sub-surface structures and deep-lying repositories are discussed. Finally, the ideas proposed for deep-lying geological repositories for nuclear wastes are discussed

Representations of some quantum tori Lie subalgebras

International Nuclear Information System (INIS)

Jiang, Jingjing; Wang, Song

2013-01-01

In this paper, we define the q-analog Virasoro-like Lie subalgebras in x ∞ =a ∞ (b ∞ , c ∞ , d ∞ ). The embedding formulas into x ∞ are introduced. Irreducible highest weight representations of A(tilde sign) q , B(tilde sign) q , and C(tilde sign) q -series of the q-analog Virasoro-like Lie algebras in terms of vertex operators are constructed. We also construct the polynomial representations of the A(tilde sign) q , B(tilde sign) q , C(tilde sign) q , and D(tilde sign) q -series of the q-analog Virasoro-like Lie algebras.

Recoupling Lie algebra and universal ω-algebra

International Nuclear Information System (INIS)

Joyce, William P.

2004-01-01

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

Review of compact, alternate concepts for magnetic confinement fusion

International Nuclear Information System (INIS)

Nickerson, S.B.; Shmayda, W.T.; Dinner, P.J.; Gierszewski, P.

1984-06-01

This report documents a study of compact alternate magnetic confinement fusion experiments and conceptual reactor designs. The purpose of this study is to identify those devices with a potential to burn tritium in the near future. The bulk of the report is made up of a review of the following compact alternates: compact toroids, high power density tokamaks, linear magnetic systems, compact mirrors, reversed field pinches and some miscellaneous concepts. Bumpy toruses and stellarators were initially reviewed but were not pursued since no compact variations were found. Several of the concepts show promise of either burning tritium or evolving into tritium burning devices by the early 1990's: RIGGATRON, Ignitor, OHTE, Frascati Tokamak upgrade, several driven (low or negative net power) mirror experiments and several Reversed Field Pinch experiments that may begin operation around 1990. Of the above only the Frascati Tokamak Upgrade has had funds allocated. Also identified in this report are groups who may have tritium burning experiments in the mid to late 1990's. There is a discussion of the differences between the reviewed devices and the mainline tokamak experiments. This discussion forms the basis of recommendations for R and D aimed at the compact alternates and the applicability of the present CFFTP program to the needs of the compact alternates. These recommendations will be presented in a subsequent report

Adélie penguin population diet monitoring by analysis of food DNA in scats.

Science.gov (United States)

Jarman, Simon N; McInnes, Julie C; Faux, Cassandra; Polanowski, Andrea M; Marthick, James; Deagle, Bruce E; Southwell, Colin; Emmerson, Louise

2013-01-01

The Adélie penguin is the most important animal currently used for ecosystem monitoring in the Southern Ocean. The diet of this species is generally studied by visual analysis of stomach contents; or ratios of isotopes of carbon and nitrogen incorporated into the penguin from its food. There are significant limitations to the information that can be gained from these methods. We evaluated population diet assessment by analysis of food DNA in scats as an alternative method for ecosystem monitoring with Adélie penguins as an indicator species. Scats were collected at four locations, three phases of the breeding cycle, and in four different years. A novel molecular diet assay and bioinformatics pipeline based on nuclear small subunit ribosomal RNA gene (SSU rDNA) sequencing was used to identify prey DNA in 389 scats. Analysis of the twelve population sample sets identified spatial and temporal dietary change in Adélie penguin population diet. Prey diversity was found to be greater than previously thought. Krill, fish, copepods and amphipods were the most important food groups, in general agreement with other Adélie penguin dietary studies based on hard part or stable isotope analysis. However, our DNA analysis estimated that a substantial portion of the diet was gelatinous groups such as jellyfish and comb jellies. A range of other prey not previously identified in the diet of this species were also discovered. The diverse prey identified by this DNA-based scat analysis confirms that the generalist feeding of Adélie penguins makes them a useful indicator species for prey community composition in the coastal zone of the Southern Ocean. Scat collection is a simple and non-invasive field sampling method that allows DNA-based estimation of prey community differences at many temporal and spatial scales and provides significant advantages over alternative diet analysis approaches.

Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations

Science.gov (United States)

Morozov, Oleg I.

2018-06-01

The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The exotic cohomology of the symmetry algebras opens a way to formulate such conditions in internal terms of the PDE s under the study. In this paper we consider certain examples of infinite-dimensional Lie algebras with nontrivial second exotic cohomology groups and show that the Maurer-Cartan forms of the associated extensions of these Lie algebras generate Lax representations for integrable systems, both known and new ones.

Being honest about dishonesty: correlating self-reports and actual lying

NARCIS (Netherlands)

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

Confirmation of Faint Dwarf Galaxies in the M81 Group

Science.gov (United States)

Chiboucas, Kristin; Jacobs, Bradley A.; Tully, R. Brent; Karachentsev, Igor D.

2013-11-01

We have followed up on the results of a 65 deg2 CFHT/MegaCam imaging survey of the nearby M81 Group searching for faint and ultra-faint dwarf galaxies. The original survey turned up 22 faint candidate dwarf members. Based on two-color HST ACS/WFC and WFPC2 photometry, we now confirm 14 of these as dwarf galaxy members of the group. Distances and stellar population characteristics are discussed for each. To a completeness limit of M_{r^{\\prime }} = -10, we find a galaxy luminosity function slope of -1.27 ± 0.04 for the M81 Group. In this region, there are now 36 M81 Group members known, including 4 blue compact dwarfs; 8 other late types including the interacting giants M81, NGC 3077, and M82; 19 early type dwarfs; and at least 5 potential tidal dwarf galaxies. We find that the dSph galaxies in M81 appear to lie in a flattened distribution, similar to that found for the Milky Way and M31. One of the newly discovered dSph galaxies has properties similar to the ultra-faint dwarfs being found in the Local Group with a size Re ~ 100 pc and total magnitude estimates M_{r^{\\prime }} = -6.8 and MI ~ -9.1.

Methods of making high performance compacts and products

International Nuclear Information System (INIS)

Fey, M.G.; Iyer, N.C.; Male, A.T.; Lovic, W.R.

1990-01-01

This patent describes a method of forming a pressed, dense compact. It comprises: providing a compactable particulate combination of: Class 1 metals selected from the group consisting of Ag, Cu, Al, and mixtures thereof, with material selected from the class consisting of CdO, SnO, SnO 2 , C, Co, Ni, Fe, Cr, Cr 3 C 2 , Cr 7 C 3 , W, WC, W 2 C, WB, Mo, Mo 2 C, MoB, Mo 2 B, TiC, TiN, TiB 2 , Si, SiC, Si 3 N 4 , and mixtures thereof; uniaxially pressing the particulate combination to provide a compact; placing at least one compact in an open pan; evacuating air from the pan; sealing the open top portion of the pan; stacking the pans next to each other, with plates having a high electrical resistance disposed between each pan so that the pans and plates alternate with each other, where a layer of thermally conductive, granular, pressure transmitting material is disposed between each pan and plate, which granular material acts to provide heat transfer and uniform mechanical loading to the compacts in the pans upon subsequent pressing; placing the stack in a press, passing an electrical current through the pans and high electrical resistance plates to cause a heating effect on the compacts in the pans, and uniaxial pressing the alternating pans and plates; cooling and releasing pressure on the alternating pans and plates; and separating the pans from the plates and the compacts from the pans

Advances in geometry and Lie algebras from supergravity

CERN Document Server

Frè, Pietro Giuseppe

2018-01-01

This book aims to provide an overview of several topics in advanced Differential Geometry and Lie Group Theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject. .

The quantum poisson-Lie T-duality and mirror symmetry

International Nuclear Information System (INIS)

Parkhomenko, S.E.

1999-01-01

Poisson-Lie T-duality in quantum N=2 superconformal Wess-Zumino-Novikov-Witten models is considered. The Poisson-Lie T-duality transformation rules of the super-Kac-Moody algebra currents are found from the conjecture that, as in the classical case, the quantum Poisson-Lie T-duality transformation is given by an automorphism which interchanges the isotropic subalgebras of the underlying Manin triple in one of the chirality sectors of the model. It is shown that quantum Poisson-Lie T-duality acts on the N=2 super-Virasoro algebra generators of the quantum models as a mirror symmetry acts: in one of the chirality sectors it is a trivial transformation while in another chirality sector it changes the sign of the U(1) current and interchanges the spin-3/2 currents. A generalization of Poisson-Lie T-duality for the quantum Kazama-Suzuki models is proposed. It is shown that quantum Poisson-Lie T-duality acts in these models as a mirror symmetry also

Lie-Hamilton systems on curved spaces: a geometrical approach

Science.gov (United States)

Herranz, Francisco J.; de Lucas, Javier; Tobolski, Mariusz

2017-12-01

A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a t-dependent vector field taking values in a finite-dimensional Lie algebra, a Vessiot-Guldberg Lie algebra, of Hamiltonian vector fields relative to a Poisson structure. Its general solution can be written as an autonomous function, the superposition rule, of a generic finite family of particular solutions and a set of constants. We pioneer the study of Lie-Hamilton systems on Riemannian spaces (sphere, Euclidean and hyperbolic plane), pseudo-Riemannian spaces (anti-de Sitter, de Sitter, and Minkowski spacetimes) as well as on semi-Riemannian spaces (Newtonian spacetimes). Their corresponding constants of motion and superposition rules are obtained explicitly in a geometric way. This work extends the (graded) contraction of Lie algebras to a contraction procedure for Lie algebras of vector fields, Hamiltonian functions, and related symplectic structures, invariants, and superposition rules.

Diffusion through statically compacted clay

International Nuclear Information System (INIS)

Ho, C.L.; Shebl, M.A.A.

1994-01-01

This paper presents experimental work on the effect of compaction on contaminant flow through clay liners. The experimental program included evaluation of soil properties, compaction, permeability and solute diffusion. A permeameter was built of non reactive materials to test samples compacted at different water contents and compactive efforts. The flow of a permeating solute, LiCl, was monitored. Effluent samples were collected for solute concentration measurements. The concentrations were measured by performing atomic adsorption tests. The analyzed results showed different diffusion characteristics when compaction conditions changed. At each compactive effort, permeability decreased as molding water content increased. Consequently, transit time (measured at relative concentration 50%) increased and diffusivity decreased. As compactive effort increased for soils compacted dry of optimum, permeability and diffusion decreased. On the other hand, as compactive effort increased for soils compacted wet of optimum, permeability and diffusivity increased. Tortuosity factor was indirectly measured from the diffusion and retardation rate. Tortuosity factor also decreased as placement water content was increased from dry of optimum to wet of optimum. Then decreases were more pronounced for low compactive effort tests. 27 refs., 7 figs., 5 tabs

Self-Compacting Concrete

OpenAIRE

Okamura, Hajime; Ouchi, Masahiro

2003-01-01

Self-compacting concrete was first developed in 1988 to achieve durable concrete structures. Since then, various investigations have been carried out and this type of concrete has been used in practical structures in Japan, mainly by large construction companies. Investigations for establishing a rational mix-design method and self-compactability testing methods have been carried out from the viewpoint of making self-compacting concrete a standard concrete.

A CATALOG OF ULTRA-COMPACT HIGH VELOCITY CLOUDS FROM THE ALFALFA SURVEY: LOCAL GROUP GALAXY CANDIDATES?

International Nuclear Information System (INIS)

Adams, Elizabeth A. K.; Giovanelli, Riccardo; Haynes, Martha P.

2013-01-01

We present a catalog of 59 ultra-compact high velocity clouds (UCHVCs) extracted from the 40% complete ALFALFA HI-line survey. The ALFALFA UCHVCs have median flux densities of 1.34 Jy km s –1 , median angular diameters of 10', and median velocity widths of 23 km s –1 . We show that the full UCHVC population cannot easily be associated with known populations of high velocity clouds. Of the 59 clouds presented here, only 11 are also present in the compact cloud catalog extracted from the commensal GALFA-HI survey, demonstrating the utility of this separate dataset and analysis. Based on their sky distribution and observed properties, we infer that the ALFALFA UCHVCs are consistent with the hypothesis that they may be very low mass galaxies within the Local Volume. In that case, most of their baryons would be in the form of gas, and because of their low stellar content, they remain unidentified by extant optical surveys. At distances of ∼1 Mpc, the UCHVCs have neutral hydrogen (H I) masses of ∼10 5 -10 6 M ☉ , H I diameters of ∼2-3 kpc, and indicative dynamical masses within the H I extent of ∼10 7 -10 8 M ☉ , similar to the Local Group ultra-faint dwarf Leo T. The recent ALFALFA discovery of the star-forming, metal-poor, low mass galaxy Leo P demonstrates that this hypothesis is true in at least one case. In the case of the individual UCHVCs presented here, confirmation of their extragalactic nature will require further work, such as the identification of an optical counterpart to constrain their distance.

Comparison of Poisson structures and Poisson-Lie dynamical r-matrices

OpenAIRE

Enriquez, B.; Etingof, P.; Marshall, I.

2004-01-01

We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices of Balog-Feher-Palla.

Isometric elbow extensors strength in supine- and prone-lying positions.

Science.gov (United States)

Abdelzaher, Ibrahim E; Ababneh, Anas F; Alzyoud, Jehad M

2013-01-01

The purpose of this study was to compare isometric strength of elbow extensors measured in supine- and prone-lying positions at elbow flexion angles of 45 and 90 degrees. Twenty-two male subjects under single-blind procedures participated in the study. Each subject participated in both supine-lying and prone-lying measuring protocols. Calibrated cable tensiometer was used to measure isometric strength of the right elbow extensors and a biofeedback electromyography was used to assure no substitution movements from shoulder girdle muscles. The mean values of isometric strength of elbow extensors measured from supine-lying position at elbow flexion angles of 45 and 90 degrees were 11.1  ±  4.2 kg and 13.1  ±  4.6 kg, while those measured from prone-lying position were 9.9  ±  3.6 kg and 12  ±  4.2 kg, respectively. There is statistical significant difference between the isometric strength of elbow extensors measured from supine-lying position at elbow flexion angles of 45 and 90 degrees compared to that measured from prone-lying position (p  isometric strength of elbow extensors since supine-lying starting position is better than prone-lying starting position.

Young children will lie to prevent a moral transgression.

Science.gov (United States)

Harvey, Teresa; Davoodi, Telli; Blake, Peter R

2018-01-01

Children believe that it is wrong to tell lies, yet they are willing to lie prosocially to adhere to social norms and to protect a listener's feelings. However, it is not clear whether children will lie instrumentally to intervene on behalf of a third party when a moral transgression is likely to occur. In three studies (N=270), we investigated the conditions under which 5- to 8-year-olds would tell an "interventional lie" in order to misdirect one child who was seeking another child in a park. In Study 1, older children lied more when the seeker intended to steal a toy from another child than when the seeker intended to give cookies to the child. In Study 2, the transgression (stealing) was held constant, but harm to the victim was either emphasized or deemphasized. Children at all ages were more likely to lie to prevent the theft when harm was emphasized. In Study 3, harm to the victim was held constant and the act of taking was described as either theft or a positive action. Children at all ages were more likely to lie when the transgression was emphasized. We conclude that by 5years of age, children are capable of lying to prevent a moral transgression but that this is most likely to occur when both the transgression and the harm to the victim are salient. Published by Elsevier Inc.

Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

Science.gov (United States)

Ray, S. Saha

2018-04-01

In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.

Compaction of Ti–6Al–4V powder using high velocity compaction technique

International Nuclear Information System (INIS)

Khan, Dil Faraz; Yin, Haiqing; Li, He; Qu, Xuanhui; Khan, Matiullah; Ali, Shujaat; Iqbal, M. Zubair

2013-01-01

Highlights: • We compacted Ti–6Al–4V powder by HVC technique. • As impact force rises up, the green density of the compacts increases gradually. • At impact force 1.857 kN relative sintered density of the compacts reaches 99.88%. • Spring back of the green compact’s decreases gradually with increasing impact force. • Mechanical properties of the samples increases with increasing impact force. - Abstract: High velocity compaction technique was applied to the compaction of pre-alloyed, hydride–dehydride Ti–6Al–4V powder. The powder was pressed in single stroke with a compaction speed of 7.10–8.70 ms −1 . When the speed was 8.70 ms −1 , the relative density of the compacts reaches up to 85.89% with a green density of 3.831 g cm −3 . The green samples were sintered at 1300 °C in Ar-gas atmosphere. Scanning electron microscope (SEM) was used to examine the surface of the sintered samples. Density and mechanical properties such as Vickers micro hardness and bending strength of the powder samples were investigated. Experimental results indicated that with the increase in impact force, the density and mechanical properties of the compacts increased. The sintered compacts exhibited a maximum relative density of 99.88% with a sintered density of 4.415 g cm −3 , hardness of 364–483 HV and the bending strength in the range of 103–126.78 MPa. The springback of the compacts decreased with increasing impact force