Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory

by Jürgen A. Fuchs

Overview

This is an introduction to the theory of affine Lie algebras and to the theory of quantum groups. It is unique in discussing these two subjects in a unified manner, which is made possible by discussing their respective applications in conformal field theory. The description of affine algebras covers the classification problem, the connection with loop algebras, and representation theory including modular properties. The necessary background from the theory of semisimple Lie algebras is also provided. The discussion of quantum groups concentrates on deformed enveloping algebras and their representation theory, but other aspects such as R-matrices and matrix quantum groups are also dealt with.

Product Details

ISBN-13:	9780521484121
Publisher:	Cambridge University Press
Publication date:	03/09/1995
Series:	Cambridge Monographs on Mathematical Physics
Edition description:	New Edition
Pages:	448
Product dimensions:	6.85(w) x 9.69(h) x 0.98(d)

Table of Contents

1. Semisimple Lie algebras; 2. Affine Lie algebras; 3. WZW theories; 4. Quantum groups; 5. Duality, fusion rules, and modular invariance; Bibliography; Index.

Editorial Reviews

"Clearly written; mathematical development is handled with wonderful care." The American Mathematical Monthly

"...serves well as an introduction to these ideas and as a stimulus to further research and communication between mathematicians and physicists." Alex Jay Feingold, Mathematical Reviews

From the Publisher