On Morita and derived equivalences for cohomological Mackey algebras

Linckelmann, M. & Rognerud, B. (2017). On Morita and derived equivalences for cohomological Mackey algebras. Mathematische Zeitschrift, doi: 10.1007/s00209-017-1942-8

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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 ofcohomological 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.

Item Type: Article
Additional Information: This is a post-peer-review, pre-copyedit version of an article published in Mathematische Zeitschrift. The final authenticated version is available online at: https://doi.org/10.1007/s00209-017-1942-8
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/18619

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