Lectures On Infinite Dimensional Lie Algebra
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Infinite Dimensional Lie Algebras
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Author : Minoru Wakimoto
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Infinite Dimensional Lie Algebras written by Minoru Wakimoto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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.
Lectures On Infinite Dimensional Lie Algebra
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Author : Minoru Wakimoto
language : en
Publisher: World Scientific
Release Date : 2001-10-26
Lectures On Infinite Dimensional Lie Algebra written by Minoru Wakimoto and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-26 with Mathematics categories.
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.
Highest Weight Representations Of Infinite Dimensional Lie Algebra
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Author : Victor G Kac
language : en
Publisher: World Scientific
Release Date : 1988-04-01
Highest Weight Representations Of Infinite Dimensional Lie Algebra written by Victor G Kac and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-04-01 with Mathematics categories.
This book is a collection of a series of lectures given by Prof. V Kac at Tata Institute, India in Dec '85 and Jan '86. These lectures focus on the idea of a highest weight representation, which goes through four different incarnations.The first is the canonical commutation relations of the infinite-dimensional Heisenberg Algebra (= oscillator algebra). The second is the highest weight representations of the Lie algebra gl∞ of infinite matrices, along with their applications to the theory of soliton equations, discovered by Sato and Date, Jimbo, Kashiwara and Miwa. The third is the unitary highest weight representations of the current (= affine Kac-Moody) algebras. These algebras appear in the lectures twice, in the reduction theory of soliton equations (KP → KdV) and in the Sugawara construction as the main tool in the study of the fourth incarnation of the main idea, the theory of the highest weight representations of the Virasoro algebra.This book should be very useful for both mathematicians and physicists. To mathematicians, it illustrates the interaction of the key ideas of the representation theory of infinite-dimensional Lie algebras; and to physicists, this theory is turning into an important component of such domains of theoretical physics as soliton theory, theory of two-dimensional statistical models, and string theory.
Infinite Dimensional Lie Algebras
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Author : Victor G. Kac
language : en
Publisher: Cambridge University Press
Release Date : 1990
Infinite Dimensional Lie Algebras written by Victor G. Kac and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
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.
Lectures On Infinite Dimensional Lie Algebra
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Author : Minoru Wakimoto
language : en
Publisher: World Scientific
Release Date : 2001
Lectures On Infinite Dimensional Lie Algebra written by Minoru Wakimoto and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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 and 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.
Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras
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Author : Victor G. Kac
language : en
Publisher: World Scientific
Release Date : 2013
Bombay Lectures On Highest Weight Representations Of Infinite Dimensional Lie Algebras written by Victor G. Kac and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
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 Groups With Applications
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Author : Victor Kac
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Infinite Dimensional Groups With Applications written by Victor Kac and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to Springer-Verlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On Landau-Lifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D. S. Freed 83 Dimensional Kahler Geometry Positive-Energy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M. A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V. G. Kac 167 Infinite-Dimensional Lie Algebras I. Kaplansky 217 Harish-Chandra Modules Over the Virasoro Algebra & L. J. Santharoubane 233 Rational Homotopy Theory of Flag S.
Infinite Dimensional Lie Algebras
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Author : Victor G. Kac
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09
Infinite Dimensional Lie Algebras written by Victor G. Kac and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Mathematics categories.
Introduction To Lie Algebras And Representation Theory
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Author : JAMES HUMPHREYS
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-10-27
Introduction To Lie Algebras And Representation Theory written by JAMES HUMPHREYS and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-27 with Mathematics categories.
This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.
Lie Algebras Of Finite And Affine Type
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Author : Roger William Carter
language : en
Publisher: Cambridge University Press
Release Date : 2005-10-27
Lie Algebras Of Finite And Affine Type written by Roger William Carter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-27 with Mathematics categories.
This book provides a thorough but relaxed mathematical treatment of Lie algebras.