New Directions in Hopf Algebras

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Overview

This timely collection of expository papers by leading researchers in the field highlights progress and new directions in Hopf algebras. The volume arises from the MSRI workshop on Hopf Algebras in October 1999, where many exciting recent developments were discussed. The work presented here will be stimulating to researchers and accessible to graduate students. 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 chapters on recent progress in classifying finite-dimensional Hopf algebras, both in the semisimple case and in the pointed case, as well as what is known about the extension theory of Hopf algebras and on important connections of Hopf algebras to Lie algebras, knot theory and operator algebras. The volume also includes Mitsuhiro Takeuchi's article 'A short course on quantum matrices', now a standard reference in spite of its relative lack of availability; it has been updated for this volume.

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Editorial Reviews

From The Critics
Nine studies explore new Hopf algebras that have arisen in such areas as mathematics, physics, and topology. Among the topics are pointed Hopf algebras, classifying finite-dimensional triangular Hopf algebras, co-ideal sub-algebras and quantum symmetric pairs, extensions and cohomology, finite quantum groupiods and their applications, Hopf algebras extensions and monoidal categories, quantum matrices, and the Brauer group of a Hopf algebra. No index is provided. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

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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