On Picard groups of blocks with normal defect groups

Michael Livesey

On Picard groups of blocks with normal defect groups

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arxiv 1907.12167 v3 pith:OOBE6LOR submitted 2019-07-29 math.RT

Michael Livesey This is my paper · ORCID

classification math.RT

keywords abeliandefectgroupsnormalauto-equivalenceblockblocksboltje

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abstract

Let $b$ be a block with normal abelian defect group and abelian inertial quotient. We prove that every Morita auto-equivalence of $b$ has linear source. We note that this improves upon results of Zhou and also Boltje, Kessar and Linckelmann.

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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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