Trivial source bimodule rings for blocks and 𝑝-permutation equivalences

Linckelmann, Markus

doi:10.1090/S0002-9947-08-04577-7

Trivial source bimodule rings for blocks and $p$-permutation equivalences
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Trans. Amer. Math. Soc. 361 (2009), 1279-1316 Request permission

Abstract:

We associate with any $p$-block of a finite group a Grothendieck ring of certain $p$-permutation bimodules. We extend the notion of $p$-permutation equivalences introduced by Boltje and Xu (2006) to source algebras of $p$-blocks of finite groups. We show that a $p$-permutation equivalence between two source algebras $A$, $B$ of blocks with a common defect group and same local structure induces an isotypy.

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