Algebras of Functions on Quantum Groups: Part I
About this Title
Leonid I. Korogodski, Institute for Advanced Study, Princeton, NJ and Yan S. Soibelman, Institute for Advanced Study, Princeton, NJ
Publication: Mathematical Surveys and Monographs
Publication Year: 1998; Volume 56
ISBNs: 978-0-8218-0336-3 (print); 978-1-4704-1284-5 (online)
MathSciNet review: MR1614943
MSC: Primary 17B37; Secondary 16W30, 58F05, 81R50
The book is devoted to the study of algebras of functions on quantum groups. The authors' approach to the subject is based on the parallels with symplectic geometry, allowing the reader to use geometric intuition in the theory of quantum groups. The book includes the theory of Poisson Lie groups (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions, and the theory of quantum Weyl groups. This book can serve as a text for an introduction to the theory of quantum groups.
Graduate students and research mathematicians working in algebra, representation theory, and mathematical physics.
Table of Contents
- 0. Introduction
- 1. Poisson Lie groups
- 2. Quantized universal enveloping algebras
- 3. Quantized algebras of functions
- 4. Quantum Weyl group and the universal quantum $R$-matrix