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.
Nicolás Andruskiewitsch, Hans-Jürgen Schneider
págs. 1-68
págs. 69-116
Coideal Subalgebras and Quantum Symmetric Pairs
Gail Letzter
págs. 117-165
Hopf Algebra Extensions and Cohomology
Akira Masuoka
págs. 167-209
Finite Quantum Groupoids and Their Applications
Dmitri Nikshych, Leonid Vainerman
págs. 211-262
David E. Radford
págs. 263-319
Hopf Algebra Extensions and Monoidal Categories
Peter Schauenburg
págs. 321-381
A Short Course on Quantum Matrices
Mitsuhiro Takeuchi
págs. 383-435
The Brauer Group of a Hopf Algebra
Freddy Van Oystaeyen, Yinhuo Zhang
págs. 437-485
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