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Infinite-Dimensional Lie Algebras - Victor G. Kac

Infinite-Dimensional Lie Algebras

Paperback

Published: 19th December 1994
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This is the third, substantially revised edition of this important monograph. The book is concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems.

'A clear account of Kac Moody algebras by one of the founders ... Eminently suitable as an introduction ... with a surprising number of exercises.' American Mathematical Monthly ' ... a useful contribution. All the basic elements of the subject are covered ... Many results which were previously scattered about in the literature are collected here ... The book also contains many exercises and useful comments ...' Physics in Canada

Basic definitions
The invariant bilinear form and the generalized Casimir operator
Integrable representations of Kac-Moody algebras and the Weyl group
A classification of generalized Cartan matrices
Real and imaginary roots
Affine algebras: the normalized invariant form, the root system, and the Weyl group
Affine algebras as central extensions of loop algebras
Twisted affine algebras and finite order automorphisms
Highest-weight modules over Kac-Moody algebras
Integrable highest-weight modules: the character formula
Integrable highest-weight modules: the weight system and the unitarizability
Integrable highest-weight modules over affine algebras
Application to n-function identities
Sugawara operators and branching functions
Affine algebras, theta functions, and modular forms
The principal and homogeneous vertex operator constructions of the basic representation
Boson-Fermion correspondence
Application to soliton equations
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521466936
ISBN-10: 0521466938
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 424
Published: 19th December 1994
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.11 x 15.75  x 2.77
Weight (kg): 0.63
Edition Number: 3
Edition Type: Revised