Introduction to Finite and Infinite Dimensional Lie Super algebras

Introduction to Finite and Infinite Dimensional Lie  Super algebras
Author: Neelacanta Sthanumoorthy
Publsiher: Academic Press
Total Pages: 512
Release: 2016-04-26
ISBN 10: 012804683X
ISBN 13: 9780128046838
Language: EN, FR, DE, ES & NL

Introduction to Finite and Infinite Dimensional Lie Super algebras Book Review:

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
Author: Minoru Wakimoto
Publsiher: American Mathematical Soc.
Total Pages: 304
Release: 2001
ISBN 10: 9780821826546
ISBN 13: 0821826549
Language: EN, FR, DE, ES & NL

Infinite dimensional Lie Algebras Book Review:

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.

Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras

Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras
Author: Victor G. Kac,Ashok K. Raina,Natasha Rozhkovskaya
Publsiher: World Scientific
Total Pages: 237
Release: 2013
ISBN 10: 9814522201
ISBN 13: 9789814522205
Language: EN, FR, DE, ES & NL

Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras Book Review:

The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras--such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations--simplify and clarify the constructions of the first edition of the book. -- Cover.

Infinite Dimensional Lie Superalgebras

Infinite Dimensional Lie Superalgebras
Author: Yuri Bahturin,Alexander V. Mikhalev,Viktor M. Petrogradsky,Mikhail V. Zaicev
Publsiher: Walter de Gruyter
Total Pages: 260
Release: 1992-01-01
ISBN 10: 3110851202
ISBN 13: 9783110851205
Language: EN, FR, DE, ES & NL

Infinite Dimensional Lie Superalgebras Book Review:

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

Automorphic Forms and Lie Superalgebras

Automorphic Forms and Lie Superalgebras
Author: Urmie Ray
Publsiher: Springer Science & Business Media
Total Pages: 278
Release: 2007-03-06
ISBN 10: 1402050100
ISBN 13: 9781402050107
Language: EN, FR, DE, ES & NL

Automorphic Forms and Lie Superalgebras Book Review:

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.

Geometry and Analysis on Finite and Infinite dimensional Lie Groups

Geometry and Analysis on Finite  and Infinite dimensional Lie Groups
Author: Aleksander Strasburger
Publsiher: Unknown
Total Pages: 357
Release: 2002
ISBN 10:
ISBN 13: UOM:39015056685145
Language: EN, FR, DE, ES & NL

Geometry and Analysis on Finite and Infinite dimensional Lie Groups Book Review:

Journal of Group Theory in Physics

Journal of Group Theory in Physics
Author: Anonim
Publsiher: Unknown
Total Pages: 329
Release: 1995
ISBN 10:
ISBN 13: UOM:39015046586403
Language: EN, FR, DE, ES & NL

Journal of Group Theory in Physics Book Review:

Lectures on Infinite Dimensional Lie Algebra

Lectures on Infinite Dimensional Lie Algebra
Author: Minoru Wakimoto
Publsiher: World Scientific
Total Pages: 456
Release: 2001-10-26
ISBN 10: 9814494003
ISBN 13: 9789814494007
Language: EN, FR, DE, ES & NL

Lectures on Infinite Dimensional Lie Algebra Book Review:

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

Mathematical Reviews

Mathematical Reviews
Author: Anonim
Publsiher: Unknown
Total Pages: 329
Release: 2008-10
ISBN 10:
ISBN 13: UOM:39015082440762
Language: EN, FR, DE, ES & NL

Mathematical Reviews Book Review:

Lie Superalgebras and Enveloping Algebras

Lie Superalgebras and Enveloping Algebras
Author: Ian Malcolm Musson
Publsiher: American Mathematical Soc.
Total Pages: 488
Release: 2012-04-04
ISBN 10: 0821868675
ISBN 13: 9780821868676
Language: EN, FR, DE, ES & NL

Lie Superalgebras and Enveloping Algebras Book Review:

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. This book develops the theory of Lie superalgebras, their enveloping algebras, and their representations. The book begins with five chapters on the basic properties of Lie superalgebras, including explicit constructions for all the classical simple Lie superalgebras. Borel subalgebras, which are more subtle in this setting, are studied and described. Contragredient Lie superalgebras are introduced, allowing a unified approach to several results, in particular to the existence of an invariant bilinear form on $\mathfrak{g}$. The enveloping algebra of a finite dimensional Lie superalgebra is studied as an extension of the enveloping algebra of the even part of the superalgebra. By developing general methods for studying such extensions, important information on the algebraic structure is obtained, particularly with regard to primitive ideals. Fundamental results, such as the Poincare-Birkhoff-Witt Theorem, are established. Representations of Lie superalgebras provide valuable tools for understanding the algebras themselves, as well as being of primary interest in applications to other fields. Two important classes of representations are the Verma modules and the finite dimensional representations. The fundamental results here include the Jantzen filtration, the Harish-Chandra homomorphism, the Sapovalov determinant, supersymmetric polynomials, and Schur-Weyl duality. Using these tools, the center can be explicitly described in the general linear and orthosymplectic cases. In an effort to make the presentation as self-contained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics.

Dualities and Representations of Lie Superalgebras

Dualities and Representations of Lie Superalgebras
Author: Shun-Jen Cheng,Weiqiang Wang
Publsiher: American Mathematical Soc.
Total Pages: 302
Release: 2012
ISBN 10: 0821891189
ISBN 13: 9780821891186
Language: EN, FR, DE, ES & NL

Dualities and Representations of Lie Superalgebras Book Review:

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.

Compact Lie Groups and Their Representations

Compact Lie Groups and Their Representations
Author: Dmitriĭ Petrovich Zhelobenko
Publsiher: American Mathematical Soc.
Total Pages: 448
Release: 1973-01-01
ISBN 10: 9780821886649
ISBN 13: 0821886649
Language: EN, FR, DE, ES & NL

Compact Lie Groups and Their Representations Book Review:

Lie Algebras Theory and Algorithms

Lie Algebras  Theory and Algorithms
Author: W.A. de Graaf
Publsiher: Elsevier
Total Pages: 408
Release: 2000-02-04
ISBN 10: 9780080535456
ISBN 13: 0080535453
Language: EN, FR, DE, ES & NL

Lie Algebras Theory and Algorithms Book Review:

The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

3rd Hellenic School Elementary Particle Physics Corfu Greece 13 30 September 1989

3rd Hellenic School Elementary Particle Physics  Corfu  Greece  13 30 September 1989
Author: E. N. Argyres,G. Zoupanos,N. D. Tracas
Publsiher: World Scientific Publishing Company Incorporated
Total Pages: 790
Release: 1990
ISBN 10:
ISBN 13: STANFORD:36105030146596
Language: EN, FR, DE, ES & NL

3rd Hellenic School Elementary Particle Physics Corfu Greece 13 30 September 1989 Book Review:

The aim of the proceedings is to give, in a comprehensive way, an introduction to the main topics in Elementary Particle Physics as well as to present current research activities on both theoretical and experimental subjects. It can be considered as a complementary volume to the proceedings of the first and second Hellenic Schools.

JMSJ

JMSJ
Author: Nihon Sūgakkai
Publsiher: Unknown
Total Pages: 329
Release: 2005
ISBN 10:
ISBN 13: UCSC:32106018249695
Language: EN, FR, DE, ES & NL

JMSJ Book Review:

Advances in Theoretical and Mathematical Physics

Advances in Theoretical and Mathematical Physics
Author: Anonim
Publsiher: Unknown
Total Pages: 329
Release: 1998
ISBN 10:
ISBN 13: UOM:39015050443509
Language: EN, FR, DE, ES & NL

Advances in Theoretical and Mathematical Physics Book Review:

New Technical Books

New Technical Books
Author: New York Public Library
Publsiher: Unknown
Total Pages: 329
Release: 1990
ISBN 10:
ISBN 13: UOM:39015063566536
Language: EN, FR, DE, ES & NL

New Technical Books Book Review:

Seminari di geometria

Seminari di geometria
Author: Anonim
Publsiher: Unknown
Total Pages: 329
Release: 2004
ISBN 10:
ISBN 13: UOM:39015059092497
Language: EN, FR, DE, ES & NL

Seminari di geometria Book Review:

Algebra Colloquium

Algebra Colloquium
Author: Anonim
Publsiher: Unknown
Total Pages: 329
Release: 2000
ISBN 10:
ISBN 13: UOM:39015053362136
Language: EN, FR, DE, ES & NL

Algebra Colloquium Book Review:

Abstracts of Papers Presented to the American Mathematical Society

Abstracts of Papers Presented to the American Mathematical Society
Author: American Mathematical Society
Publsiher: Unknown
Total Pages: 329
Release: 2007
ISBN 10:
ISBN 13: CORNELL:31924099691275
Language: EN, FR, DE, ES & NL

Abstracts of Papers Presented to the American Mathematical Society Book Review: