Cohomology of invariant Drinfeld twists on group algebras

Details Cohomology of invariant Drinfeld twists on group algebras Cohomology of invariant Drinfeld twists on group algebras

2009-03-16

arxiv.org/abs/0903.2807v2

International Mathematics Research Notices (2009), Article ID rnp209

Mathematics

Quantum Algebra

28 pages. Shorter proofs, additional references

Scientific paper

10.1093/imrn/rnp209

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 outer automorphisms of G induced by conjugation in the group algebra 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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