Morita equivalence classes of blocks with elementary abelian defect groups of order 16

Charles W. Eaton

Morita equivalence classes of blocks with elementary abelian defect groups of order 16

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arxiv 1612.03485 v4 pith:72737IE6 submitted 2016-12-11 math.GR

Charles W. Eaton This is my paper · ORCID

classification math.GR

keywords defectblocksabelianclasseselementaryequivalencegroupgroups

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abstract

We classify the Morita equivalence classes of blocks with elementary abelian defect groups of order $16$ with respect to a complete discrete valuation ring with algebraically closed residue field of characteristic two. As a consequence, blocks with this defect group are derived equivalent to their Brauer correspondent in the normalizer of a defect group and so satisfy Brou\'e's Conjecture.

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Morita equivalence classes of blocks with elementary abelian defect groups of order 32
math.RT 2019-08 conditional novelty 7.0 of 10

Blocks with elementary abelian defect group (C2)^5 are shown to be Morita equivalent to exactly one of 34 listed block algebras, and Harada's conjecture is verified for them.

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