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Picard groups of blocks and Donovan’s conjecture

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17th Meeting: Groups & Their Applications

While the outer automorphism group of a block over an algebraically closed field of characteristic p is usually an infinite group, it was recently observed by Boltje, Kessar and Linckelmann that the outer automorphism group of a block defined over a suitable discrete valuation ring is finite in all known examples.

As of yet there is no general explanation for the finiteness of these outer automorphism groups, and the closely related Picard groups of blocks. I will talk about recent results on the structure of these groups, and an application to Donovan’s conjecture (which is joint work with C. Eaton and M. Livesey).

This talk is part of the Algebra Seminar series.

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