Trivial source bimodule rings for blocks and $p$-permutation equivalences
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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.References
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Additional Information
- Markus Linckelmann
- Affiliation: Department of Mathematical Sciences, University of Aberdeen, Meston Building, Aberdeen, AB24 3UE, United Kingdom
- MR Author ID: 240411
- Received by editor(s): December 14, 2006
- Published electronically: October 10, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 1279-1316
- MSC (2000): Primary 20C20
- DOI: https://doi.org/10.1090/S0002-9947-08-04577-7
- MathSciNet review: 2457399