Skip to main content
SpringerLink
Log in
Book cover

Quantum Groups and Their Representations

  • Book
  • © 1997

Overview

Authors:
  1. Anatoli Klimyk

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

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Konrad Schmüdgen

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

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Greater concentration on physical problems than any other comparable books

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

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
      Download chapter PDF

    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
      Download chapter PDF

    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
      Download chapter PDF

    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
      Download chapter PDF

    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
    Download chapter PDF
Back to top

Keywords

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.

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

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

Publish with us

Policies and ethics

Back to top

Search

Navigation