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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Trivial source bimodule rings for blocks and $ p$-permutation equivalences


Author: Markus Linckelmann
Journal: Trans. Amer. Math. Soc. 361 (2009), 1279-1316
MSC (2000): Primary 20C20
Published electronically: October 10, 2008
MathSciNet review: 2457399
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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.


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Additional Information

Markus Linckelmann
Affiliation: Department of Mathematical Sciences, University of Aberdeen, Meston Building, Aberdeen, AB24 3UE, United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04577-7
PII: S 0002-9947(08)04577-7
Received by editor(s): December 14, 2006
Published electronically: October 10, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.