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Quantum Groups and Their Representations

  • Anatoli Klimyk
  • Konrad Schmüdgen

Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. An Introduction to Quantum Groups

    1. Front Matter
      Pages 1-1
    2. Anatoli Klimyk, Konrad Schmüdgen
      Pages 3-36
    3. Anatoli Klimyk, Konrad Schmüdgen
      Pages 37-52
    4. Anatoli Klimyk, Konrad Schmüdgen
      Pages 53-96
    5. Anatoli Klimyk, Konrad Schmüdgen
      Pages 97-132
    6. Anatoli Klimyk, Konrad Schmüdgen
      Pages 133-154
  3. Quantized Universal Enveloping Algebras

    1. Front Matter
      Pages 155-155
    2. Anatoli Klimyk, Konrad Schmüdgen
      Pages 157-196
    3. Anatoli Klimyk, Konrad Schmüdgen
      Pages 197-242
    4. Anatoli Klimyk, Konrad Schmüdgen
      Pages 243-300
  4. Quantized Algebras of Functions

    1. Front Matter
      Pages 301-301
    2. Anatoli Klimyk, Konrad Schmüdgen
      Pages 303-330
    3. Anatoli Klimyk, Konrad Schmüdgen
      Pages 331-394
    4. Anatoli Klimyk, Konrad Schmüdgen
      Pages 395-454
  5. Noncommutative Differential Calculus

    1. Front Matter
      Pages 455-455
    2. Anatoli Klimyk, Konrad Schmüdgen
      Pages 457-472
    3. Anatoli Klimyk, Konrad Schmüdgen
      Pages 473-490
    4. Anatoli Klimyk, Konrad Schmüdgen
      Pages 491-528
  6. Back Matter
    Pages 529-552

About this book

Introduction

This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers.
The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.

Keywords

Vector space algebra representation theory theoretical physics

Authors and affiliations

  • Anatoli Klimyk
    • 1
  • Konrad Schmüdgen
    • 2
  1. 1.Institute for Theoretical PhysicsUkrainian Academy of SciencesKievUkraine
  2. 2.Fakultät für Mathematik und InformatikUniversität LeipzigLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-60896-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-64601-0
  • Online ISBN 978-3-642-60896-4
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site