New Directions in Hopf Algebras [Paperback]

This book contains survey articles for graduate students and researchers on various topics surrounding Hopf algebras.This volume of articles arising from the MSRI workshop on Hopf Algebras in October 1999 forms a broad survey of this exciting field and its connection with quantum groups and related areas. Topics include pointed Hopf algebras, triangular Hopf algebras, Hopf algebra extensions and cohomology, quantum groups and groupoids, quantum symmetric pairs, monoidal categories, and the Brauer group of a Hopf algebra. The volume also includes an updated version of Mitsuhiro Takeuchi's article A short course on quantum matrices , now a standard reference in the field.This volume of articles arising from the MSRI workshop on Hopf Algebras in October 1999 forms a broad survey of this exciting field and its connection with quantum groups and related areas. Topics include pointed Hopf algebras, triangular Hopf algebras, Hopf algebra extensions and cohomology, quantum groups and groupoids, quantum symmetric pairs, monoidal categories, and the Brauer group of a Hopf algebra. The volume also includes an updated version of Mitsuhiro Takeuchi's article A short course on quantum matrices , now a standard reference in the field.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.1. Pointed Hopf algebras Nicolas Andruskiewitsch and Hans-Jurgen Schneider; 2. On the classification of finilÂ