Affine Lie Algebras and Quantum Groups

ISBN-13: 9780521484121 / Angielski / Miękka / 1995 / 448 str.

Jurgen Fuchs

Opis

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.

Recenzje

'… 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

Spis treści

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