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On Morita and derived equivalences for cohomological Mackey algebras

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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.

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Acknowledgements

M. Linckelmann would like to acknowledge support from the EPSRC Grant EP/M02525X/1. M. Linckelmann and B. Rognerud would like to thank the EPFL for its hospitality during the special research semester on Local Representation Theory and Simple Groups in 2016.

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Authors and Affiliations

  1. Department of Mathematics, University of London, EC1V OHB, London, UK

    Markus Linckelmann

  2. Institut de Recherche Mathmatique Avance, Université de Strasbourg, UMR 7501, 67084, Strasbourg Cedex, France

    Baptiste Rognerud

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  1. Markus Linckelmann
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  2. Baptiste Rognerud
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Correspondence to Baptiste Rognerud.

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Linckelmann, M., Rognerud, B. On Morita and derived equivalences for cohomological Mackey algebras. Math. Z. 289, 39–50 (2018). https://doi.org/10.1007/s00209-017-1942-8

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  • DOI: https://doi.org/10.1007/s00209-017-1942-8

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