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Quantum Groups and Their Representations (Theoretical and Mathematical Physics)

✍ Scribed by Anatoli Klimyk, Konrad Schmüdgen

Publisher
Springer
Year
1998
Tongue
English
Leaves
582
Edition
1
Category
Library
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✦ Synopsis

This book provides a treatment of the theory of quantum groups (quantized universal enveloping algebras and quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The theory of the simplest and most important quantum groups and their representations is presented in detail. A number of topics and results from the more advanced general theory are developed and discussed. Many applications in mathematical and theoretical physics are indicated. The book starts as an introduction for the beginner and continues at a textbook level for graduate students in physics and in mathematics. It may serve as a reference for more advanced readers.

✦ Table of Contents

Table of Contents (Hyperlinked)......Page 1
Subject Index......Page 10
1. Hopf Algebras......Page 20
2. q-Calculus......Page 54
3. The Quantum Algebra Uq(sl2) and Its Representations......Page 70
4. The Quantum Group SLq(2) and Its Representations......Page 114
5. The q-Oscillator Algebras and Their Representations......Page 150
6. Drinfeld-Jimbo Algebras......Page 174
7. Finite-Dimensional Representations of Drinfeld— Jimbo Algebras......Page 214
8. Quasitriangularity and Universal R-Matrices......Page 260
9. Coordinate Algebras of Quantum Groups and Quantum Vector Spaces......Page 320
10. Coquasitriangularity and Crossed Product Constructions......Page 348
11. Corepresentation Theory and Compact Quantum Groups......Page 412
12. Covariant Differential Calculus on Quantum Spaces......Page 474
13. Hopf Bimodules and Exterior Algebras......Page 490
14. Covariant Differential Calculus on Quantum Groups......Page 508
Bibliography......Page 545
Subject Index......Page 562
Table of Contents......Page 569
Title Page......Page 581

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