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arXiv · 2008.05857

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

Michael Livesey·Claudio Marchi
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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.

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Michael Livesey, Claudio Marchi. 2020-08-13. Picard groups for blocks with normal defect groups and linear source bimodules. https://arxiv.org/abs/2008.05857

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