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 -permutation equivalences

Author: Markus Linckelmann
Journal: Trans. Amer. Math. Soc. 361 (2009), 1279-1316
MSC (2000): Primary 20C20
DOI: https://doi.org/10.1090/S0002-9947-08-04577-7
Published electronically: October 10, 2008
MathSciNet review: 2457399
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Abstract: We associate with any -block of a finite group a Grothendieck ring of certain -permutation bimodules. We extend the notion of -permutation equivalences introduced by Boltje and Xu (2006) to source algebras of -blocks of finite groups. We show that a -permutation equivalence between two source algebras , of blocks with a common defect group and same local structure induces an isotypy.

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