Hardcover ISBN:  9780821803363 
Product Code:  SURV/56 
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eBook ISBN:  9781470412845 
Product Code:  SURV/56.E 
List Price:  $125.00 
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AMS Member Price:  $100.00 
Hardcover ISBN:  9780821803363 
eBook: ISBN:  9781470412845 
Product Code:  SURV/56.B 
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AMS Member Price:  $203.20 $153.20 
Hardcover ISBN:  9780821803363 
Product Code:  SURV/56 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412845 
Product Code:  SURV/56.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821803363 
eBook ISBN:  9781470412845 
Product Code:  SURV/56.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 56; 1998; 150 ppMSC: Primary 17; Secondary 16; 81
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.
ReadershipGraduate students and research mathematicians working in algebra, representation theory, and mathematical physics.

Table of Contents

Chapters

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


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


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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.
Graduate students and research mathematicians working in algebra, representation theory, and mathematical physics.

Chapters

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

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