Introduction To Finite And Infinite Dimensional Lie Super Algebras

Author : Neelacanta Sthanumoorthy
Publisher : Academic Press
Page : 512 pages
File Size : 43,9 Mb
Release : 2016-04-26
Category : Mathematics
ISBN : 9780128046838

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Introduction to Finite and Infinite Dimensional Lie (Super)algebras by Neelacanta Sthanumoorthy Pdf

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

Author : Minoru Wakimoto
Publisher : American Mathematical Soc.
Page : 332 pages
File Size : 46,9 Mb
Release : 2001
Category : Mathematics
ISBN : 0821826549

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Infinite-dimensional Lie Algebras by Minoru Wakimoto Pdf

This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of ...... 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.

Author : Victor G. Kac
Publisher : Springer Science & Business Media
Page : 267 pages
File Size : 40,9 Mb
Release : 2013-11-09
Category : Mathematics
ISBN : 9781475713824

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Infinite Dimensional Lie Algebras by Victor G. Kac Pdf

Author : Ivan Penkov,Crystal Hoyt
Publisher : Springer Nature
Page : 245 pages
File Size : 47,9 Mb
Release : 2022-01-05
Category : Mathematics
ISBN : 9783030896607

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Classical Lie Algebras at Infinity by Ivan Penkov,Crystal Hoyt Pdf

Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.

Author : D.B. Fuks
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468487657

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Cohomology of Infinite-Dimensional Lie Algebras by D.B. Fuks Pdf

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.

Author : Karl-Hermann Neeb,Arturo Pianzola
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 43,7 Mb
Release : 2010-10-17
Category : Mathematics
ISBN : 9780817647414

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Developments and Trends in Infinite-Dimensional Lie Theory by Karl-Hermann Neeb,Arturo Pianzola Pdf

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.

Author : M. Scheunert
Publisher : Springer
Page : 280 pages
File Size : 50,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540352860

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The Theory of Lie Superalgebras by M. Scheunert Pdf

Author : Shun-Jen Cheng,Weiqiang Wang
Publisher : American Mathematical Soc.
Page : 323 pages
File Size : 55,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821891186

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Dualities and Representations of Lie Superalgebras by Shun-Jen Cheng,Weiqiang Wang Pdf

This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation theory of Lie superalgebras. Several folklore results are rigorously proved (and occasionally corrected in detail), sometimes with new proofs. Three important dualities are presented in the book, with the unifying theme of determining irreducible characters of Lie superalgebras. In order of increasing sophistication, they are Schur duality, Howe duality, and super duality. The combinatorics of symmetric functions is developed as needed in connections to Harish-Chandra homomorphism as well as irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is presented from scratch with complete detail. Howe duality for Lie superalgebras is presented in book form for the first time. Super duality is a new approach developed in the past few years toward understanding the Bernstein-Gelfand-Gelfand category of modules for classical Lie superalgebras. Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras and thus gives a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.

Author : Minoru Wakimoto
Publisher : World Scientific
Page : 456 pages
File Size : 42,9 Mb
Release : 2001-10-26
Category : Mathematics
ISBN : 9789814494007

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Lectures On Infinite-dimensional Lie Algebra by Minoru Wakimoto Pdf

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.

Author : Victor G. Kac
Publisher : Cambridge University Press
Page : 428 pages
File Size : 46,8 Mb
Release : 1990
Category : Mathematics
ISBN : 0521466938

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Infinite-Dimensional Lie Algebras by Victor G. Kac Pdf

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.

Author : Gerard G. A. Bäuerle,Eddy A. Kerf,A. P. E. ten Kroode
Publisher : North Holland
Page : 420 pages
File Size : 48,9 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015021636272

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Lie Algebras by Gerard G. A. Bäuerle,Eddy A. Kerf,A. P. E. ten Kroode Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 49,9 Mb
Release : 2024-06-02
Category : Electronic
ISBN : 9789814507721

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Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras by Anonim Pdf

Author : Yuri Bahturin,Alexander V. Mikhalev,Viktor M. Petrogradsky,Mikhail V. Zaicev
Publisher : Walter de Gruyter
Page : 261 pages
File Size : 55,9 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110851205

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Infinite Dimensional Lie Superalgebras by Yuri Bahturin,Alexander V. Mikhalev,Viktor M. Petrogradsky,Mikhail V. Zaicev Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Author : Augustin Banyaga,Joshua A Leslie,Thierry Robart
Publisher : World Scientific
Page : 176 pages
File Size : 46,5 Mb
Release : 2002-07-12
Category : Science
ISBN : 9789814488143

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Infinite Dimensional Lie Groups in Geometry and Representation Theory by Augustin Banyaga,Joshua A Leslie,Thierry Robart Pdf

This book constitutes the proceedings of the 2000 Howard conference on “Infinite Dimensional Lie Groups in Geometry and Representation Theory”. It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and established researchers in the field of geometry and its applications to mathematical physics. Contents:Inheritance Properties for Lipschitz-Metrizable Frölicher Groups (J Teichmann)Around the Exponential Mapping (T Robart)On a Solution to a Global Inverse Problem with Respect to Certain Generalized Symmetrizable Kac-Moody Algebras (J A Leslie)The Lie Group of Fourier Integral Operators on Open Manifolds (R Schmid)On Some Properties of Leibniz Algebroids (A Wade)On the Geometry of Locally Conformal Symplectic Manifolds (A Banyaga)Some Properties of Locally Conformal Symplectic Manifolds (S Haller)Criticality of Unit Contact Vector Fields (P Rukimbira)Orbifold Homeomorphism and Diffeomorphism Groups (J E Borzellino & V Brunsden)A Note on Isotopies of Symplectic and Poisson Structures (A Banyaga & P Donato)Remarks on Actions on Compacta by Some Infinite-Dimensional Groups (V Pestov) Readership: Graduate students and researchers in mathematics and mathematical physics. Keywords:

Author : Stephen Berman,Paul Fendley,Yi-Zhi Huang,Kailash Misra,Brian Parshall
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 54,8 Mb
Release : 2002
Category : Conformal invariants
ISBN : 9780821827161

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Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory by Stephen Berman,Paul Fendley,Yi-Zhi Huang,Kailash Misra,Brian Parshall Pdf

Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ``Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.