Int. Math. Res. Not. 2010 (2010), 1894--1939; doi:10.1093/imrn/rnp209 (46 pages)

Pierre Guillot and Christian Kassel

Cohomology of invariant Drinfeld twists on group algebras

Mathematics Subject Classification (2000): 20D25, 20J06, 16S34, 16W30

Abstract. We show how to compute a certain group of equivalence classes of invariant Drinfeld twists on the algebra of a finite group G over a field k of characteristic zero. This group is naturally isomorphic to the second lazy cohomology group of the Hopf algebra of k-valued functions on G. When k is algebraically closed, the answer involves the group of class-preserving outer automorphisms of G as well as the set of all pairs (A, b), where A is an abelian normal subgroup of G and b is a k*-valued G-invariant non-degenerate alternating bilinear form on the Pontryagin dual of A. We give a number of examples.

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(16 juin 2010)