New Directions in Hopf Algebras

This book contains survey articles for graduate students and researchers on various topics surrounding Hopf algebras.

Susan Montgomery (Edited by), Hans-Jurgen Schneider (Edited by)

9780521124317, Cambridge University Press

Paperback, published 3 December 2009

496 pages
23.4 x 15.6 x 2.5 cm, 0.69 kg

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.

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.

Subject Areas: Applied mathematics [PBW], Algebra [PBF]