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Quantum Groups and Their Representations

  • Book
  • © 1997

Overview

Authors:
  1. Anatoli Klimyk

    1. Institute for Theoretical Physics, Ukrainian Academy of Sciences, Kiev, Ukraine

  2. Konrad Schmüdgen

    1. Fakultät für Mathematik und Informatik, Universität Leipzig, Leipzig, Germany

  • Greater concentration on physical problems than any other comparable books

Part of the book series: Theoretical and Mathematical Physics (TMP)

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About this book

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.

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-XIX
    Download chapter PDF

  2. An Introduction to Quantum Groups

    1. Front Matter

      Pages 1-1
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    2. Hopf Algebras

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 3-36

    3. q-Calculus

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 37-52

    4. The Quantum Algebra U q (sl2)and Its Representations

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 53-96

    5. The Quantum Group SL q (2) and Its Representations

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 97-132

    6. The q-Oscillator Algebras and Their Representations

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 133-154

  3. Quantized Universal Enveloping Algebras

    1. Front Matter

      Pages 155-155
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    2. Drinfeld-Jimbo Algebras

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 157-196

    3. Finite-Dimensional Representations of Drinfeld-Jimbo Algebras

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 197-242

    4. Quasitriangularity and Universal R-Matrices

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 243-300

  4. Quantized Algebras of Functions

    1. Front Matter

      Pages 301-301
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    2. Coordinate Algebras of Quantum Groups and Quantum Vector Spaces

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 303-330

    3. Coquasitriangularity and Crossed Product Constructions

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 331-394

    4. Corepresentation Theory and Compact Quantum Groups

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 395-454

  5. Noncommutative Differential Calculus

    1. Front Matter

      Pages 455-455
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    2. Covariant Differential Calculus on Quantum Spaces

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 457-472

    3. Hopf Bimodules and Exterior Algebras

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 473-490

    4. Covariant Differential Calculus on Quantum Groups

      • Anatoli Klimyk, Konrad Schmüdgen
      Pages 491-528

  6. Back Matter

    Pages 529-552
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Reviews

From the reviews
"Klimyk and Schmüdgen are kind to their readers. Proofs are given in full, and there are helpful explanations of the basic concepts ... the book has the virtue of comprehensivness in its chose range of topics. It is easy to dip into and use as a reference book." (A. Sudbery, Bulletin of the London Mathematical Society, 2000)

Authors and Affiliations

  • Institute for Theoretical Physics, Ukrainian Academy of Sciences, Kiev, Ukraine

    Anatoli Klimyk

  • Fakultät für Mathematik und Informatik, Universität Leipzig, Leipzig, Germany

    Konrad Schmüdgen

Accessibility Information

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Bibliographic Information

  • Book Title: Quantum Groups and Their Representations

  • Authors: Anatoli Klimyk, Konrad Schmüdgen

  • Series Title: Theoretical and Mathematical Physics

  • DOI: https://doi.org/10.1007/978-3-642-60896-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-642-64601-0Published: 14 December 2011

  • eBook ISBN: 978-3-642-60896-4Published: 06 December 2012

  • Series ISSN: 1864-5879

  • Series E-ISSN: 1864-5887

  • Edition Number: 1

  • Number of Pages: XX, 552

  • Topics: Mathematical Methods in Physics, Group Theory and Generalizations

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