Equivalences between blocks of cohomological Mackey algebras

Let G be a finite group and (K, O, k) be a p-modular system “large enough”. Let R = O or k. There is a bijection between the blocks of the group algebra RG and the central primitive idempotents (the blocks) of the so-called cohomological Mackey algebra coμR(G). Here, we prove that a so-called permeable derived equivalence between two blocks of group algebras implies the existence of a derived equivalence between the corresponding blocks of cohomological Mackey algebras. In particular, in the context of Broué’s abelian defect group conjecture, if two blocks are splendidly derived equivalent, then the corresponding blocks of cohomological Mackey algebras are derived equivalent.


Published in:
Mathematische Zeitschrift, 280, 1, 421–449
Year:
2015
Publisher:
Heidelberg, Springer Verlag
ISSN:
0025-5874
Keywords:
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 Record created 2015-04-23, last modified 2018-09-13

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