[PDF] Cohomology Of Infinite Dimensional Lie Algebras Download

Cohomology of Infinite Dimensional Lie Algebras PDF
Author: D.B. Fuks
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Size: 17.88 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 352
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Cohomology Of Infinite Dimensional Lie Algebras

Book by D.B. Fuks, Cohomology Of Infinite Dimensional Lie Algebras Books available in PDF, EPUB, Mobi Format. Download Cohomology Of Infinite Dimensional Lie Algebras books, There is no question that the cohomology of infinite dimensional Lie algebras deserves a brief and separate mono graph. This subject is not cover~d by any of the tradition al branches of mathematics and is characterized by relative ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to "recognize" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list. There are classifica tion theorems in the theory of infinite-dimensional Lie al gebras as well, but they are encumbered by strong restric tions of a technical character. These theorems are useful mainly because they yield a considerable supply of interest ing examples. We begin with a list of such examples, and further direct our main efforts to their study.




[PDF] Infinite Dimensional Lie Algebras Download

Infinite Dimensional Lie Algebras PDF
Author: Victor G. Kac
Publisher: Cambridge University Press
Release Date: 1990
Size: 37.71 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 400
View: 5436

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Infinite Dimensional Lie Algebras

Book by Victor G. Kac, Infinite Dimensional Lie Algebras Books available in PDF, EPUB, Mobi Format. Download Infinite Dimensional Lie Algebras books, The third, substantially revised edition of a monograph concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie albegras, and their representations, based on courses given over a number of years at MIT and in Paris. Suitable for graduate courses.




[PDF] Infinite Dimensional Lie Algebras Download

Infinite dimensional Lie Algebras PDF
Author: Minoru Wakimoto
Publisher: American Mathematical Soc.
Release Date: 2001
Size: 32.38 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 304
View: 6685

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Infinite Dimensional Lie Algebras

Book by Minoru Wakimoto, Infinite Dimensional Lie Algebras Books available in PDF, EPUB, Mobi Format. Download Infinite Dimensional Lie Algebras books, This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of ${\widehat {\mathfrak {sl}}}(2, {\mathbb C})$, root systems, the Cartan matrix, and a Dynkin diagram of a finite-dimensional simple Lie algebra. Continuing on, the main subjects of the book are the structure (real and imaginary root systems) of and the character formula for Kac-Moody superalgebras, which is explained in a very general setting. Only elementary linear algebra and group theory are assumed. Also covered is modular property and asymptotic behavior of integrable characters of affine Lie algebras. The exposition is self-contained and includes examples. The book can be used in a graduate-level course on the topic.




[PDF] Lie Algebras Part 2 Download

Lie Algebras  Part 2 PDF
Author: E.A. de Kerf
Publisher: Elsevier
Release Date: 1997-10-30
Size: 36.38 MB
Format: PDF, Mobi
Category : Science
Languages : en
Pages : 553
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Lie Algebras Part 2

Book by E.A. de Kerf, Lie Algebras Part 2 Books available in PDF, EPUB, Mobi Format. Download Lie Algebras Part 2 books, This is the long awaited follow-up to Lie Algebras, Part I which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part II deals mainly with the representations and applications of Lie Algebras and contains many cross references to Part I. The theoretical part largely deals with the representation theory of Lie algebras with a triangular decomposition, of which Kac-Moody algebras and the Virasoro algebra are prime examples. After setting up the general framework of highest weight representations, the book continues to treat topics as the Casimir operator and the Weyl-Kac character formula, which are specific for Kac-Moody algebras. The applications have a wide range. First, the book contains an exposition on the role of finite-dimensional semisimple Lie algebras and their representations in the standard and grand unified models of elementary particle physics. A second application is in the realm of soliton equations and their infinite-dimensional symmetry groups and algebras. The book concludes with a chapter on conformal field theory and the importance of the Virasoro and Kac-Moody algebras therein.




[PDF] Lie Algebras Download

Lie Algebras PDF
Author: Gerard G. A. Bäuerle
Publisher: North Holland
Release Date: 1990
Size: 19.57 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 394
View: 4660

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Lie Algebras

Book by Gerard G. A. Bäuerle, Lie Algebras Books available in PDF, EPUB, Mobi Format. Download Lie Algebras books, The structure of the laws in physics is largely based on symmetries. This book is on Lie algebras, the mathematics of symmetry. It has grown from lectures for undergraduates in theoretical and mathematical physics and 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. The new series ''Studies in Mathematical Physics'' aims at discussing recent developments in physics offering sound mathematics and a high didactical quality. The emphasis lies on techniques, ideas and methods that are fundamental, interesting and innovating in both mathematics and physics, herewith creating a link between the two disciplines.




[PDF] Lectures On Infinite Dimensional Lie Algebra Download

Lectures on Infinite Dimensional Lie Algebra PDF
Author: Minoru Wakimoto
Publisher: World Scientific
Release Date: 2001-10-26
Size: 16.15 MB
Format: PDF, Docs
Category : Science
Languages : en
Pages : 456
View: 715

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Lectures On Infinite Dimensional Lie Algebra

Book by Minoru Wakimoto, Lectures On Infinite Dimensional Lie Algebra Books available in PDF, EPUB, Mobi Format. Download Lectures On Infinite Dimensional Lie Algebra books, The representation theory of affine Lie algebras has been developed in close connection with various areas of mathematics and mathematical physics in the last two decades. There are three excellent books on it, written by Victor G Kac. This book begins with a survey and review of the material treated in Kac's books. In particular, modular invariance and conformal invariance are explained in more detail. The book then goes further, dealing with some of the recent topics involving the representation theory of affine Lie algebras. Since these topics are important not only in themselves but also in their application to some areas of mathematics and mathematical physics, the book expounds them with examples and detailed calculations. Contents:Preliminaries on Affine Lie AlgebrasCharacters of Integrable RepresentationsPrincipal Admissible WeightsResidue of Principal Admissible CharactersCharacters of Affine OrbifoldsOperator CalculusBranching FunctionsW-AlgebraVertex Representations for Affine Lie AlgebrasSoliton Equations Readership: Graduate students and researchers interested in representation theory, combinatorics, vertex algebras, modular forms, soliton equations, particle physics and solvable models. Keywords:Admissible Representation;Principal Admissible Weight;Modular Transformation;Vertex Algebra;Lambda-Bracket;W-Algebra;Fusion Algebra;Affine Orbifold;Soliton Equation;Hirota Bilinear Differential EquationReviews: “The material from this book is very important for graduate students and researchers in mathematics and theoretical physics. It can also be used as a starting point for further research in the representation theory of infinite-dimensional Lie algebras and vertex algebras.” Mathematical Reviews




[PDF] Infinite Dimensional Lie Algebras Download

Infinite dimensional Lie Algebras PDF
Author: R.K. Amayo
Publisher: Springer
Release Date: 1974-10-31
Size: 15.32 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 425
View: 7715

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Infinite Dimensional Lie Algebras

Book by R.K. Amayo, Infinite Dimensional Lie Algebras Books available in PDF, EPUB, Mobi Format. Download Infinite Dimensional Lie Algebras books, It is only in recent times that infinite-dimensional Lie algebras have been the subject of other than sporadic study, with perhaps two exceptions: Cartan's simple algebras of infinite type, and free algebras. However, the last decade has seen a considerable increase of interest in the subject, along two fronts: the topological and the algebraic. The former, which deals largely with algebras of operators on linear spaces, or on manifolds modelled on linear spaces, has been dealt with elsewhere*). The latter, which is the subject of the present volume, exploits the surprising depth of analogy which exists between infinite-dimen sional Lie algebras and infinite groups. This is not to say that the theory consists of groups dressed in Lie-algebraic clothing. One of the tantalising aspects of the analogy, and one which renders it difficult to formalise, is that it extends to theorems better than to proofs. There are several cases where a true theorem about groups translates into a true theorem about Lie algebras, but where the group-theoretic proof uses methods not available for Lie algebras and the Lie-theoretic proof uses methods not available for groups. The two theories tend to differ in fine detail, and extra variations occur in the Lie algebra case according to the underlying field. Occasionally the analogy breaks down altogether. And of course there are parts of the Lie theory with no group-theoretic counterpart.




[PDF] Introduction To Finite And Infinite Dimensional Lie Super Algebras Download

Introduction to Finite and Infinite Dimensional Lie  Super algebras PDF
Author: Neelacanta Sthanumoorthy
Publisher: Academic Press
Release Date: 2016-04-26
Size: 70.80 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 512
View: 5423

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Introduction To Finite And Infinite Dimensional Lie Super Algebras

Book by Neelacanta Sthanumoorthy, Introduction To Finite And Infinite Dimensional Lie Super Algebras Books available in PDF, EPUB, Mobi Format. Download Introduction To Finite And Infinite Dimensional Lie Super Algebras books, Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras




[PDF] Developments And Trends In Infinite Dimensional Lie Theory Download

Developments and Trends in Infinite Dimensional Lie Theory PDF
Author: Karl-Hermann Neeb
Publisher: Birkhäuser
Release Date: 2010-10-28
Size: 51.58 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 492
View: 4577

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Developments And Trends In Infinite Dimensional Lie Theory

Book by Karl-Hermann Neeb, Developments And Trends In Infinite Dimensional Lie Theory Books available in PDF, EPUB, Mobi Format. Download Developments And Trends In Infinite Dimensional Lie Theory books, This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.




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