Infinite-Dimensional Lie Algebras / Edition 3

by Victor G. Kac

Overview

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.

Product Details

ISBN-13:	9780521466936
Publisher:	Cambridge University Press
Publication date:	08/26/1994
Edition description:	Revised
Pages:	424
Product dimensions:	5.98(w) x 9.02(h) x 0.94(d)

Table of Contents

Introduction; Notational conventions; 1. Basic definitions; 2. The invariant bilinear form and the generalized casimir operator; 3. Integrable representations of Kac-Moody algebras and the weyl group; 4. A classification of generalized cartan matrices; 5. Real and imaginary roots; 6. Affine algebras: the normalized cartan invariant form, the root system, and the weyl group; 7. Affine algebras as central extensions of loop algebras; 8. Twisted affine algebras and finite order automorphisms; 9. Highest-weight modules over Kac-Moody algebras; 10. Integrable highest-weight modules: the character formula; 11. Integrable highest-weight modules: the weight system and the unitarizability; 12. Integrable highest-weight modules over affine algebras; 13. Affine algebras, theta functions, and modular forms; 14. The principal and homogeneous vertex operator constructions of the basic representation; Index of notations and definitions; References; Conference proceedings and collections of paper.

Editorial Reviews

'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

From the Publisher