Infinite-Dimensional Lie Algebras

Name: Infinite-Dimensional Lie Algebras
Price: 58.41 USD
Availability: InStock
ISBN: 9780521466936

ISBN-10: 0521466938

ISBN-13: 9780521466936

Edition: 3rd 1994 (Revised)

Authors: Victor G. Kac

List price: $68.99

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Description:

This is the third, substantially revised edition of this important monograph by a giant in the field of mathematics. The book is concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. Each chapter begins with a motivating discussion and ends with a collection of exercises with hints to the more challenging problems. The theory has applications in many areas of mathematics, and Lie algebras have been significant in the study of fundamental particles, including string theory, so this book should appeal to mathematical physicists, as well as mathematicians.

Book details

List price: $68.99
Edition: 3rd
Copyright year: 1994
Publisher: Cambridge University Press
Publication date: 8/26/1994
Binding: Paperback
Pages: 424
Size: 5.98" wide x 9.02" long x 0.94" tall
Weight: 1.364




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