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Quantum Groups

Proceedings of the 8th International Workshop on Mathematical Physics Held at the Arnold Sommerfeld Institute, Clausthal, FRG, on 19–26 July 1989

  • Editors
  • H. -D. Doebner
  • J. -D. Hennig
Conference proceedings

Part of the Lecture Notes in Physics book series (LNP, volume 370)

Table of contents

  1. Front Matter
    PDF
  2. Introduction to quantum groups
    L. A. Takhtajan
    Pages 3-28
  3. Mathematical guide to quantum groups
    H. D. Doebner, J. D. Hennig, W. Lücke
    Pages 29-63
  4. A q-boson realization of the quantum group SUq(2) and the theory of q-tensor operators
    L. C. Biedenharn
    Pages 67-88
  5. Polynomial basis for SU(2)q and Clebsch-Gordan coefficients
    H. Ruegg
    Pages 89-95
  6. Uq(sl(2)) Invariant operators and reduced polynomial identities
    A. Ch. Ganchev, V. B. Petkova
    Pages 96-106
  7. Classification and characters of Uq(sl(3, C ))representations
    V. K. Dobrev
    Pages 107-117
  8. Extremal projectors for quantized kac-moody superalgebras and some of their applications
    V. N. Tolstoy
    Pages 118-125
  9. Yang-Baxter algebras, integrable theories and Betre Ansatz
    H. J. De Vega
    Pages 129-182
  10. Yang-Baxter algebra — Bethe Ansatz — conformal quantum field theories — quantum groups
    M. Karowski
    Pages 183-218
  11. Classical Yang-Baxter equations and quantum integrable systems (Gaudin models)
    Branislav Jurčo
    Pages 219-227
  12. Quantum groups as symmetries of chiral conformal algebras
    Ivan T. Todorov
    Pages 231-277
  13. Comments on rational conformal field theory, quantum groups and tower of algebras
    César Gómez
    Pages 278-306
  14. Chern-Simons field theory and quantum groups
    E. Guadagnini, M. Martellini, M. Mintchev
    Pages 307-317
  15. Quantum symmetry associated with braid group statistics
    K. -H. Rehren
    Pages 318-339
  16. Sum rules for spins in (2 + 1)-dimensional quantum field theory
    Klaus Fredenhagen
    Pages 340-348
  17. Anomalies from the phenomenological and geometrical points of view
    N. A. Papadopoulos
    Pages 349-371
  18. KMS states, cyclic cohomology and supersymmetry
    D. Kastler
    Pages 375-397
  19. Gauge theories based on a non-commutative geometry
    Richard Kerner
    Pages 398-425
  20. Algebras symmetries spaces
    A. Jadczyk
    Pages 426-434

About these proceedings

Introduction

A thorough analysis of exactly soluble models in nonlinear classical systems and in quantum systems as well as recent studies in conformal quantum field theory have revealed the structure of quantum groups to be an interesting and rich framework for mathematical and physical problems. In this book, for the first time, authors from different schools review in an intelligible way the various competing approaches: inverse scattering methods, 2-dimensional statistical models, Yang-Baxter algebras, the Bethe ansatz, conformal quantum field theory, representations, braid group statistics, noncommutative geometry, and harmonic analysis.

Keywords

algebra cohomology conformal field theory differential equation field field theory geometry invariant partial differential equation polynomial quantum field quantum field theory scattering supersymmetry tensor

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-53503-9
  • Copyright Information Springer-Verlag 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-53503-4
  • Online ISBN 978-3-540-46647-5
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361
  • Buy this book on publisher's site