UNIVERSITY OF CALIFORNIA

"Invariant Drinfeld twists on group algebras", International Workshop/Special Session of CMS Summer Meeting 2009 "Groups and Hopf Algebras", St. John's, Newfoundland, Canada (5 June 2009)

Abstract: Drinfeld twists were introduced by Drinfeld in his work on quasi-Hopf algebras; they have been used to classify certain classes of (co)semisimple Hopf algebras. In joint work with Pierre Guillot (arXiv:0903.2807), after observing that the invariant Drinfeld twists on a Hopf algebra form a group, we determine this group when the Hopf algebra is the algebra of a finite group G. The answer involves the group of class-preserving outer automorphisms of G as well as all abelian normal subgroups of G of central type. In my lecture I shall also present several examples for which the group of invariant twists has been completely computed by us. 

"Hopf Galois extensions up to homotopy", Second joint meeting of AMS, DMV, ÖMG, Mainz, Germany (16-19 June 2005)

Abstract: (Joint work with Hans-Jürgen Schneider) Hopf Galois extensions are noncommutative analogues of principal fibre bundles with structural group replaced by a Hopf algebra. I discuss a concept of homotopy for Hopf Galois extensions and show how it allows a certain classification of such extensions. In particular, we determine all Hopf Galois extensions up to homotopy in the case when the Hopf algebra is a Drinfeld-Jimbo quantum enveloping algebra.