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Lectures on Algebraic Quantum Groups

  • Ken A. Brown
  • Ken R. Goodearl

Part of the Advanced Courses in Mathematics CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Ken A. Brown, Ken R. Goodearl
    Pages 1-14
  3. Ken A. Brown, Ken R. Goodearl
    Pages 15-23
  4. Ken A. Brown, Ken R. Goodearl
    Pages 25-28
  5. Ken A. Brown, Ken R. Goodearl
    Pages 29-37
  6. Ken A. Brown, Ken R. Goodearl
    Pages 39-44
  7. Ken A. Brown, Ken R. Goodearl
    Pages 45-58
  8. Ken A. Brown, Ken R. Goodearl
    Pages 59-67
  9. Ken A. Brown, Ken R. Goodearl
    Pages 69-80
  10. Ken A. Brown, Ken R. Goodearl
    Pages 81-91
  11. Ken A. Brown, Ken R. Goodearl
    Pages 93-96
  12. Ken A. Brown, Ken R. Goodearl
    Pages 97-101
  13. Ken A. Brown, Ken R. Goodearl
    Pages 103-111
  14. Ken A. Brown, Ken R. Goodearl
    Pages 113-117
  15. Ken A. Brown, Ken R. Goodearl
    Pages 119-123
  16. Ken A. Brown, Ken R. Goodearl
    Pages 125-127
  17. Ken A. Brown, Ken R. Goodearl
    Pages 129-133
  18. Ken A. Brown, Ken R. Goodearl
    Pages 135-146
  19. Ken A. Brown, Ken R. Goodearl
    Pages 147-158
  20. Ken A. Brown, Ken R. Goodearl
    Pages 159-164
  21. Ken A. Brown, Ken R. Goodearl
    Pages 165-172
  22. Ken A. Brown, Ken R. Goodearl
    Pages 173-183
  23. Ken A. Brown, Ken R. Goodearl
    Pages 185-193
  24. Ken A. Brown, Ken R. Goodearl
    Pages 195-203
  25. Ken A. Brown, Ken R. Goodearl
    Pages 205-213
  26. Ken A. Brown, Ken R. Goodearl
    Pages 215-227
  27. Ken A. Brown, Ken R. Goodearl
    Pages 229-235
  28. Ken A. Brown, Ken R. Goodearl
    Pages 237-245
  29. Ken A. Brown, Ken R. Goodearl
    Pages 247-254
  30. Ken A. Brown, Ken R. Goodearl
    Pages 255-258
  31. Ken A. Brown, Ken R. Goodearl
    Pages 259-272
  32. Ken A. Brown, Ken R. Goodearl
    Pages 273-280
  33. Ken A. Brown, Ken R. Goodearl
    Pages 281-288
  34. Ken A. Brown, Ken R. Goodearl
    Pages 289-302
  35. Ken A. Brown, Ken R. Goodearl
    Pages 303-311
  36. Ken A. Brown, Ken R. Goodearl
    Pages 313-321
  37. Ken A. Brown, Ken R. Goodearl
    Pages 323-330
  38. Back Matter
    Pages 331-350

About this book

Introduction

In September 2000, at the Centre de Recerca Matematica in Barcelona, we pre­ sented a 30-hour Advanced Course on Algebraic Quantum Groups. After the course, we expanded and smoothed out the material presented in the lectures and inte­ grated it with the background material that we had prepared for the participants; this volume is the result. As our title implies, our aim in the course and in this text is to treat selected algebraic aspects of the subject of quantum groups. Sev­ eral of the words in the previous sentence call for some elaboration. First, we mean to convey several points by the term 'algebraic' - that we are concerned with algebraic objects, the quantized analogues of 'classical' algebraic objects (in contrast, for example, to quantized versions of continuous function algebras on compact groups); that we are interested in algebraic aspects of the structure of these objects and their representations (in contrast, for example, to applications to other areas of mathematics); and that our tools will be drawn primarily from noncommutative algebra, representation theory, and algebraic geometry. Second, the term 'quantum groups' itself. This label is attached to a large and rapidly diversifying field of mathematics and mathematical physics, originally launched by developments around 1980 in theoretical physics and statistical me­ chanics. It is a field driven much more by examples than by axioms, and so resists attempts at concise description (but see Chapter 1. 1 and the references therein).

Keywords

algebra algebraic group quantum groups representation theory ring theory

Authors and affiliations

  • Ken A. Brown
    • 1
  • Ken R. Goodearl
    • 2
  1. 1.Department of MathematicsUniversity of GlasgowGlasgowUK
  2. 2.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA

Bibliographic information