Picard groups for blocks with normal defect groups and linear source bimodules

2020/08/13 by Livesey, Michael, Marchi, Claudio
#20C20 (Primary) 16D90 (Secondary) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2008.05857

Abstract

It is an open problem as to whether any bimodule inducing a Morita auto-equivalence of a block must have endopermutation source. We prove that, for blocks b with normal defect groups in odd characteristic, a stronger result holds, namely that all such bimodules have linear source. We also prove the analogous result in characteristic 2, provided that the defect group is of a specific, slightly restrictive, form.

Related

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• On stable equivalences with endopermutation source
• Linear source invertible bimodules and Green correspondence
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