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New Directions in Hopf Algebras

$68.00

Part of Mathematical Sciences Research Institute Publications

Nicolas Andruskiewitsch, Hans-Jurgen Schneider, Shlomo Gelaki, Gail Letzter, Akira Masuoka, Dmitri Nikshych, Leonid Vainerman, David Radford, Peter Schauenburg, Mitsuhiro Takeuchi, Fred Van Oystaeyen, Yinhuo Zhang
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  • Date Published: December 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521124317

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  • This timely collection of expository papers highlights progress and new directions in Hopf algebras. Arising from the MSRI workshop on Hopf Algebras in October 1999, some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to recent work in quantum groups. In particular, there are articles on recent progress in classifying finite-dimensional Hopf algebras, both in the semisimple case and in the pointed case. The volume also includes an updated version of Mitsuhiro Takeuchi's article "A short course on quantum matrices", now a standard reference in spite of its relative lack of availability.

    • Contributors are all top researchers
    • Expository articles on recent research developments will help graduate students enter the field
    • Includes an updated version of Mitsuhiro Takeuchi's classic article 'A short course on quantum matrices'
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    Product details

    • Date Published: December 2009
    • format: Paperback
    • isbn: 9780521124317
    • length: 496 pages
    • dimensions: 234 x 156 x 25 mm
    • weight: 0.69kg
    • availability: Available
  • Table of Contents

    1. Pointed Hopf algebras Nicolas Andruskiewitsch and Hans-Jurgen Schneider
    2. On the classification of finite-dimensional triangular Hopf algebras Shlomo Gelaki
    3. Coideal subalgebras and quantum symmetric pairs Gail Letzter
    4. Hopf algebra extensions and cohomology Akira Masuoka
    5. Finite quantum groupoids and their applications Dmitri Nikshych and Leonid Vainerman
    6. On quantum algebras and coalgebras, oriented quantum algebras and coalgebras, invariants of 1-1 tangles, knots, and links David Radford
    7. Hopf algebra extensions and monoidal categories Peter Schauenburg
    8. A short course on quantum matrices Mitsuhiro Takeuchi
    9. The Brauer group of a Hopf algebra Fred Van Oystaeyen and Yinhuo Zhang.

  • Editors

    Susan Montgomery, University of Southern California

    Hans-Jurgen Schneider, Universität Munchen

    Contributors

    Nicolas Andruskiewitsch, Hans-Jurgen Schneider, Shlomo Gelaki, Gail Letzter, Akira Masuoka, Dmitri Nikshych, Leonid Vainerman, David Radford, Peter Schauenburg, Mitsuhiro Takeuchi, Fred Van Oystaeyen, Yinhuo Zhang

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