Classifying 2-blocks with an elementary abelian defect group

Duration: 27 mins 42 secs

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Description:	Ardito, C Thursday 9th January 2020 - 17:00 to 17:30


Created:	2020-01-14 08:54
Collection:	Groups, representations and applications: new perspectives
Publisher:	Isaac Newton Institute
Copyright:	Ardito, C
Language:	eng (English)


Abstract:	Donovan's conjecture predicts that given a p-group D there are only finitely many Morita equivalence classes of blocks of group algebras of finite groups 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, Külshammer and Sambale when D is an elementary abelian 2-group, and in 2018 by Eaton, Eisele 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 O has been achieved when p=2 for abelian D with rank 3 or less, and for D=(C2)4.In my PhD thesis I have done (C2)5, and I have partial results on (C2)6. I will introduce the topic, give some definitions and then describe the process of classifying these blocks, with a focus on the process and the tools needed to produce a complete classification. All the obtained data is available on https://wiki.manchester.ac.uk/blocks/.

Abstract:

Donovan's conjecture predicts that given a p-group D there are only finitely many Morita equivalence classes of blocks of group algebras of finite groups 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, Külshammer and Sambale when D is an elementary abelian 2-group, and in 2018 by Eaton, Eisele 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 O has been achieved when p=2 for abelian D with rank 3 or less, and for D=(C2)4.In my PhD thesis I have done (C2)5, and I have partial results on (C2)6. I will introduce the topic, give some definitions and then describe the process of classifying these blocks, with a focus on the process and the tools needed to produce a complete classification. All the obtained data is available on https://wiki.manchester.ac.uk/blocks/.

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