Advanced Courses in Mathematics - CRM Barcelona

Lectures on Algebraic Quantum Groups

Authors: Brown, John C, Goodearl, Ken R.

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  • ISBN 978-3-0348-8205-7
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Softcover $54.95
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About this Textbook

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


Table of contents (36 chapters)

  • Beginnings and First Examples

    Brown, Ken A. (et al.)

    Pages 1-14

  • Further Quantized Coordinate Rings

    Brown, Ken A. (et al.)

    Pages 15-23

  • The Quantized Enveloping Algebra of sl2(k)

    Brown, Ken A. (et al.)

    Pages 25-28

  • The Finite Dimensional Representations of U q (sl2(k))

    Brown, Ken A. (et al.)

    Pages 29-37

  • Primer on Semisimple Lie Algebras

    Brown, Ken A. (et al.)

    Pages 39-44

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-0348-8205-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.95
price for USA
  • ISBN 978-3-7643-6714-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Algebraic Quantum Groups
Authors
Series Title
Advanced Courses in Mathematics - CRM Barcelona
Copyright
2002
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8205-7
DOI
10.1007/978-3-0348-8205-7
Softcover ISBN
978-3-7643-6714-5
Series ISSN
2297-0304
Edition Number
1
Number of Pages
IX, 348
Number of Illustrations and Tables
2 b/w illustrations
Topics