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Quantum Groups and Their Primitive Ideals

  • Anthony Joseph

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 29)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Anthony Joseph
    Pages 1-7
  3. Anthony Joseph
    Pages 8-35
  4. Anthony Joseph
    Pages 36-61
  5. Anthony Joseph
    Pages 62-95
  6. Anthony Joseph
    Pages 96-130
  7. Anthony Joseph
    Pages 131-160
  8. Anthony Joseph
    Pages 161-200
  9. Anthony Joseph
    Pages 201-232
  10. Anthony Joseph
    Pages 233-261
  11. Anthony Joseph
    Pages 262-293
  12. Anthony Joseph
    Pages 294-325
  13. Back Matter
    Pages 326-383

About this book

Introduction

by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule. A third principle is to focus attention on the tensor structure of the cat­ egory of (!; modules. This means of course just defining an algebra structure on Rq[G]; but this is to be done in a very specific manner. Concretely the category is required to be braided and this forces (9.4.2) the existence of an "R-matrix" satisfying in particular the quantum Yang-Baxter equation and from which the algebra structure of Rq[G] can be written down (9.4.5). Finally there was a search for a perfectly self-dual model for Rq[G] which would then be isomorphic to Uq(g). Apparently this failed; but V. G. Drinfeld found that it could be essentially made to work for the "Borel part" of Uq(g) denoted U (b) and further found a general construction (the Drinfeld double) q mirroring a Lie bialgebra. This gives Uq(g) up to passage to a quotient. One of the most remarkable aspects of the above superficially different ap­ proaches is their extraordinary intercoherence. In particular they essentially all lead for G semisimple to the same and hence "canonical", objects Rq[G] and Uq(g), though this epithet may as yet be premature.

Keywords

Algebra Kristallbasen Lie algebra Quantengruppen crystal bases einhüllende Algebren von Lie Algebren enveloping algebras of Lie algrebras quantum groups

Authors and affiliations

  • Anthony Joseph
    • 1
    • 2
  1. 1.Department of Theoretical MathematicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.Laboratoire de Mathématiques FondamentalesUniversité Pierre et Marie CurieParis Cédex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-78400-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-78402-6
  • Online ISBN 978-3-642-78400-2
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site