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Introduction To Finite And Infinite Dimensional Lie Superalgebras

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Introduction to Finite and Infinite Dimensional Lie Super algebras

Introduction to Finite and Infinite Dimensional Lie  Super algebras Book
Author : Neelacanta Sthanumoorthy
Publisher : Academic Press
Release : 2016-04-26
ISBN : 012804683X
Language : En, Es, Fr & De

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Book Description :

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

Infinite dimensional Lie Algebras

Infinite dimensional Lie Algebras Book
Author : Minoru Wakimoto
Publisher : American Mathematical Soc.
Release : 2001
ISBN : 9780821826546
Language : En, Es, Fr & De

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Book Description :

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.

Infinite Dimensional Lie Superalgebras

Infinite Dimensional Lie Superalgebras Book
Author : Yuri Bahturin,Alexander V. Mikhalev,Viktor M. Petrogradsky,Mikhail V. Zaicev
Publisher : Walter de Gruyter
Release : 1992-01-01
ISBN : 3110851202
Language : En, Es, Fr & De

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Book Description :

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

Geometry and Analysis on Finite and Infinite dimensional Lie Groups

Geometry and Analysis on Finite  and Infinite dimensional Lie Groups Book
Author : Aleksander Strasburger
Publisher : Unknown
Release : 2002
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Geometry and Analysis on Finite and Infinite dimensional Lie Groups book written by Aleksander Strasburger, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Automorphic Forms and Lie Superalgebras

Automorphic Forms and Lie Superalgebras Book
Author : Urmie Ray
Publisher : Springer Science & Business Media
Release : 2007-03-06
ISBN : 1402050100
Language : En, Es, Fr & De

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Book Description :

This book provides the reader with the tools to understand the ongoing classification and construction project of Lie superalgebras. It presents the material in as simple terms as possible. Coverage specifically details Borcherds-Kac-Moody superalgebras. The book examines the link between the above class of Lie superalgebras and automorphic form and explains their construction from lattice vertex algebras. It also includes all necessary background information.

Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2008
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan Book
Author : Nihon Sūgakkai
Publisher : Unknown
Release : 2005
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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New Technical Books

New Technical Books Book
Author : New York Public Library
Publisher : Unknown
Release : 1990
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download New Technical Books book written by New York Public Library, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Seminari di geometria

Seminari di geometria Book
Author : Anonim
Publisher : Unknown
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Advances in Theoretical and Mathematical Physics

Advances in Theoretical and Mathematical Physics Book
Author : Anonim
Publisher : Unknown
Release : 1998
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Algebra Colloquium

Algebra Colloquium Book
Author : Anonim
Publisher : Unknown
Release : 2000
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Abstracts of Papers Presented to the American Mathematical Society

Abstracts of Papers Presented to the American Mathematical Society Book
Author : American Mathematical Society
Publisher : Unknown
Release : 2005
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Unconventional Lie Algebras

Unconventional Lie Algebras Book
Author : D. B. Fuks
Publisher : American Mathematical Society(RI)
Release : 1993
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This book contains eight papers on representations and cohomology of Lie algebras. The Lie algebras here are either infinite-dimensional, are defined over fields of finite characteristic, or are actually Lie superalgebras or quantum groups. Among the topics covered here are generalizations of the Virasoro algebra, representation theory of the Virasoro algebra and of Kac-Moody algebras, cohomology of Lie algebras of vector fields on the line, and Lie superalgebras of vector fields. The paper by Retakh and Shander contains a generalization of the Schwarz derivative to the noncommutative case.

Resenhas IME USP

Resenhas IME USP Book
Author : Anonim
Publisher : Unknown
Release : 2003
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Journal of mathematics of Kyoto University

Journal of mathematics of Kyoto University Book
Author : Kyōto Daigaku
Publisher : Unknown
Release : 1997
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Character Theory of Finite Groups

Character Theory of Finite Groups Book
Author : Bertram Huppert
Publisher : De Gruyter
Release : 1998
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Varies from I. M. Isaacs' 1976 book of the same title by updating results, describing new directions the field has taken, being just a bit more module-theoretic, and including many examples in which the character table or at least the character degrees of groups are calculated. Areas in which the earlier work is still current are treated briefly if at all. Most of the material should be accessible to readers with only one term of instruction in group theory. A sampling of topics turns up degrees of irreducible representations, coprime action, Clifford Theory, monomial groups, the degree graph, lengths of conjugacy classes, splitting fields, and three arithmetical applications. Annotation copyrighted by Book News, Inc., Portland, OR

UC Santa Cruz

UC Santa Cruz Book
Author : University of California, Santa Cruz
Publisher : Unknown
Release : 2006
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Soviet Journal of Nuclear Physics

Soviet Journal of Nuclear Physics Book
Author : Anonim
Publisher : Unknown
Release : 1991
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Introduction to Vertex Operator Algebras and Their Representations

Introduction to Vertex Operator Algebras and Their Representations Book
Author : James Lepowsky,Haisheng Li
Publisher : Springer Science & Business Media
Release : 2004
ISBN : 9780817634087
Language : En, Es, Fr & De

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Book Description :

The deep and relatively new field of vertex operator algebras is intimately related to a variety of areas in mathematics and physics: for example, the concepts of "monstrous moonshine," infinite-dimensional Lie theory, string theory, and conformal field theory. This book introduces the reader to the fundamental theory of vertex operator algebras and its basic techniques and examples. Beginning with a detailed presentation of the theoretical foundations and proceeding to a range of applications, the text includes a number of new, original results and also highlights and brings fresh perspective to important works of many researchers. After introducing the elementary "formal calculus'' underlying the subject, the book provides an axiomatic development of vertex operator algebras and their modules, expanding on the early contributions of R. Borcherds, I. Frenkel, J. Lepowsky, A. Meurman, Y.-Z. Huang, C. Dong, Y. Zhu and others. The concept of a "representation'' of a vertex (operator) algebra is treated in detail, following and extending the work of H. Li; this approach is used to construct important families of vertex (operator) algebras and their modules. Requiring only a familiarity with basic algebra, Introduction to Vertex Operator Algebras and Their Representations will be useful for graduate students and researchers in mathematics and physics. The booka??s presentation of the core topics will equip readers to embark on many active research directions related to vertex operator algebras, group theory, representation theory, and string theory.

Proceedings of the National Academy of Sciences of the United States of America

Proceedings of the National Academy of Sciences of the United States of America Book
Author : National Academy of Sciences (U.S.)
Publisher : Unknown
Release : 1984
ISBN : 0987650XXX
Language : En, Es, Fr & De

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