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New Directions in Hopf Algebras

Part of Mathematical Sciences Research Institute Publications

Editors:
Susan Montgomery, University of Southern California
Hans-Jurgen Schneider, Universität Munchen

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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Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the 1970s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras (semisimple and non-semisimple), as well as what is known about the extension theory of Hopf algebras. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields.
- 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.
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Editors
Susan Montgomery, University of Southern California
Hans-Jurgen Schneider, Universität Munchen
Series editor Cam Learning use ONLY
Mathematical Sciences Research Institute
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