New Directions in Hopf Algebras

by Edited by Susan Montgomery , Hans-Jurgen Schneider

• ISBN13: 9780521815123
• ISBN10: 0521815126
• Format: Hardcover
• Copyright: 2002-05-06
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface	ix
Pointed Hopf Algebras	1	(68)
Nicolas Andruskiewitsch
Hans-Jurgen Schneider
On the Classification of Finite-Dimensional Triangular Hopf Algebras	69	(48)
Shlomo Gelaki
Coideal Subalgebras and Quantum Symmetric Pairs	117	(50)
Gail Letzter
Hopf Algebra Extensions and Cohomology	167	(44)
Akira Masuoka
Finite Quantum Groupoids and Their Applications	211	(52)
Dmitri Nikshych
Leonid Vainerman
On Quantum Algebras and Coalgebras, Oriented Quantum Algebras and Coalgebras, Invariants of 1-1 Tangles, Knots, and Links	263	(58)
David Radford
Hopf Algebra Extensions and Monoidal Categories	321	(62)
Peter Schauenburg
A Short Course on Quantum Matrices	383	(54)
Mitsuhiro Takeuchi
The Brauer Group of a Hopf Algebra	437
Fred Van Oystaeyen
Yinhuo Zhang