Mathematical Surveys and Monographs 1998; 150 pp; hardcover Volume: 56 ISBN10: 0821803360 ISBN13: 9780821803363 List Price: US$60 Member Price: US$48 Order Code: SURV/56
 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 (quasiclassical 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. Readership Graduate students and research mathematicians working in algebra, representation theory, and mathematical physics. Reviews "The book is written carefully and clearly. Every chapter begins with a short review of its content and ends with some historical remarks. All definitions are explained by several illustrative examples, remarks and comments. Proofs are given in detail. The book contains many interesting exercises. Hence we are certain that the book should be interesting for graduate students ... it should also be useful for mathematicians working in the area of abstract algebras or representation theory and for anyone who is interested in the study of quantization procedures and symplectic geometry."  Mathematical Reviews Table of Contents  Introduction
 Poisson Lie groups
 Quantized universal enveloping algebras
 Quantized algebras of functions
 Quantum Weyl group and the universal quantum \(R\)matrix
 Bibliography
