### On automorphism groups of finite group algebras

Algebra and Geometry Seminar

18th October 2017, 2:30 pm – 3:30 pm

Howard House, 4th Floor Seminar Room

The automorphism group of a finite-dimensional algebra over an algebraically closed field is an algebraic group. By contrast, the automorphism group of a finite group algebra over a p-adic ring with finite residue field is a finite group. The structure of the automorphism group of a finite group algebra over a p-local domain with an algebraically closed residue field is largely unknown; it seems to be unknown in general whether this group is finite. We identify a 'large' subgroup of this automorphism group in terms of the fusion systems of blocks of finite group algebras as well as their Dade groups. The background motivation is the - to date open - question whether Morita equivalent block algebras have isomorphic defect groups and fusion systems.

This is joint work with Robert Boltje and Radha Kessar.

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