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arXiv · 1609.07870

On Morita and derived equivalences for cohomological Mackey algebras

Markus Linckelmann·Baptiste Rognerud
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Abstract

By results of the second author, a source algebra equivalence between two $p$-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived equivalence between two blocks induces a derived equivalence between the corresponding categories of cohomological Mackey functors. The main result of this paper proves a partial converse: an equivalence (resp. Rickard equivalence) between the categories of cohomological Mackey functors of two blocks of finite groups induces a permeable Morita (resp. derived) equivalence between the two block algebras.

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BibTeXRIS

Markus Linckelmann, Baptiste Rognerud. 2016-09-26. On Morita and derived equivalences for cohomological Mackey algebras. https://arxiv.org/abs/1609.07870

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