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

This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Jürgen A. Fuchs (Author)

9780521484121, Cambridge University Press

Paperback, published 9 March 1995

448 pages, 40 b/w illus.
24.6 x 17.4 x 2.5 cm, 0.777 kg

'… a very valuable book … of interest to mathematicians and physicists working in the areas of conformal field theory, representation theory of infinite-dimensional Lie algebras and vertex operator algebras.' Drazen Adomovic, Zentralblatt für Mathematik

This is an introduction to the theory of affine Lie algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered 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. This book will be of interest to researchers and graduate students in theoretical physics and applied mathematics.

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

Subject Areas: Physics [PH]