University of Birmingham > Talks@bham > Birmingham and Warwick Algebra Seminar  > Classifying 2-blocks with an elementary abelian defect group

Classifying 2-blocks with an elementary abelian defect group

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Donovan’s conjecture predicts that given a p-group D there are only finitely many Morita equivalence classes of blocks of group algebras with defect group D. While the conjecture is still open for a generic p-group D, it has been proven in 2014 by Eaton, Kessar, K¨ulshammer and Sambale when D is an elementary abelian 2-group, and in 2018 by Eaton and Livesey when D is any abelian 2-group. The proof, however, does not describe these equivalence classes explicitly.

A classification up to Morita equivalence over a complete discrete valuation ring \mathcal O has been achieved for D with rank 3 or less, and for D = (C2)4. I have done (C2)5 and, I have partial results on (C2)6. I will introduce the topic, give the relevant definitions and then describe the process of classifying these blocks, with a particular focus on the individual tools needed to achieve a complete classification.

This talk is part of the Birmingham and Warwick Algebra Seminar series.

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