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arXiv · 2405.20268

On Morita equivalences with endopermutation source and isotypies

Xin Huang
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Abstract

We introduce a new type of equivalence between blocks of finite group algebras called an almost isotypy. An almost isotypy restricts to a weak isotypy in Brou\'{e}'s original definition, and it is slightly weaker than Linckelmann's version. We show that a bimodule of two block algebras of finite groups - which has an endopermutation module as a source and which induces a Morita equivalence - gives rise, via slash functors, to an almost isotypy if the character values of a (hence any) source are rational integers. Consequently, if two blocks are Morita equivalent via a bimodule with endopermutation source, then they are almost isotypic. We also explain why the notion of almost isotypies is reasonable.

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Xin Huang. 2024-05-30. On Morita equivalences with endopermutation source and isotypies. https://arxiv.org/abs/2405.20268

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