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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

  • Conference proceedings
  • © 1990

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Editors:
  1. H. -D. Doebner
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  2. J. -D. Hennig
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Part of the book series: Lecture Notes in Physics (LNP, volume 370)

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Table of contents (19 papers)

  1. Front Matter

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  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 SU q (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. U q (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
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Quantum Groups

  • Book Subtitle: 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

  • Series Title: Lecture Notes in Physics

  • DOI: https://doi.org/10.1007/3-540-53503-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1990

  • Softcover ISBN: 978-3-662-13787-1Published: 17 April 2014

  • eBook ISBN: 978-3-540-46647-5Published: 07 July 2005

  • Series ISSN: 0075-8450

  • Series E-ISSN: 1616-6361

  • Edition Number: 1

  • Number of Pages: X, 438

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Quantum Physics, Quantum Information Technology, Spintronics

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