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Lectures on Algebraic Quantum Groups

  • Textbook
  • © 2002

Overview

Authors:
  1. Ken A. Brown

    1. Department of Mathematics, University of Glasgow, Glasgow, UK

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    You can also search for this author in PubMed   Google Scholar

  2. Ken R. Goodearl

    1. Department of Mathematics, University of California, Santa Barbara, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (36 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Beginnings and First Examples

    • Ken A. Brown, Ken R. Goodearl
    Pages 1-14

  3. Further Quantized Coordinate Rings

    • Ken A. Brown, Ken R. Goodearl
    Pages 15-23

  4. The Quantized Enveloping Algebra of sl2(k)

    • Ken A. Brown, Ken R. Goodearl
    Pages 25-28

  5. The Finite Dimensional Representations of U q (sl2(k))

    • Ken A. Brown, Ken R. Goodearl
    Pages 29-37

  6. Primer on Semisimple Lie Algebras

    • Ken A. Brown, Ken R. Goodearl
    Pages 39-44

  7. Structure and Representation Theory of U q (g)with q Generic

    • Ken A. Brown, Ken R. Goodearl
    Pages 45-58

  8. Generic Quantized Coordinate Rings of Semisimple Groups

    • Ken A. Brown, Ken R. Goodearl
    Pages 59-67

  9. O q (G) is a Noetherian Domain

    • Ken A. Brown, Ken R. Goodearl
    Pages 69-80

  10. Bialgebras and Hopf Algebras

    • Ken A. Brown, Ken R. Goodearl
    Pages 81-91

  11. R-Matrices

    • Ken A. Brown, Ken R. Goodearl
    Pages 93-96

  12. The Diamond Lemma

    • Ken A. Brown, Ken R. Goodearl
    Pages 97-101

  13. Filtered and Graded Rings

    • Ken A. Brown, Ken R. Goodearl
    Pages 103-111

  14. Polynomial Identity Algebras

    • Ken A. Brown, Ken R. Goodearl
    Pages 113-117

  15. Skew Polynomial Rings Satisfying a Polynomial Identity

    • Ken A. Brown, Ken R. Goodearl
    Pages 119-123

  16. Homological Conditions

    • Ken A. Brown, Ken R. Goodearl
    Pages 125-127

  17. Links and Blocks

    • Ken A. Brown, Ken R. Goodearl
    Pages 129-133

  18. The Prime Spectrum

    • Ken A. Brown, Ken R. Goodearl
    Pages 135-146

  19. Stratification

    • Ken A. Brown, Ken R. Goodearl
    Pages 147-158

  20. Proof of the Stratification Theorem

    • Ken A. Brown, Ken R. Goodearl
    Pages 159-164
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Keywords

About this book

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).

Reviews

"The proofs, sketches of proofs, and quotations from the literature are carefully written. Numerous examples and exercises are included, and bibliographical notes conclude each chapter. The second and third parts end with a discussion of open problems and perspectives for further research."

--Mathematical Reviews

Authors and Affiliations

  • Department of Mathematics, University of Glasgow, Glasgow, UK

    Ken A. Brown

  • Department of Mathematics, University of California, Santa Barbara, USA

    Ken R. Goodearl

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