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On simple modules over twisted finite category algebras


Authors: Markus Linckelmann and Michał Stolorz
Journal: Proc. Amer. Math. Soc. 140 (2012), 3725-3737
MSC (2010): Primary 16D60, 18B40
DOI: https://doi.org/10.1090/S0002-9939-2012-11381-4
Published electronically: March 8, 2012
MathSciNet review: 2944713
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Abstract: The purpose of this paper is to show that the recent proof by Ganyushkin, Mazorchuk and Steinberg of the parametrisation of simple modules over finite semigroup algebras due to Clifford, Munn and Ponizovskiĭ carries over to twisted finite category algebras. We observe that the parametrisations of simple modules over Brauer algebras, Temperley-Lieb algebras, and Jones algebras due to Graham and Lehrer can be obtained as special cases of our main result. We further note that the notion of weights in the context of Alperin's weight conjecture extends to twisted finite category algebras.


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Markus Linckelmann
Affiliation: Department of Mathematics, University of Aberdeen, Aberdeen, AB24 3UE Scotland, United Kingdom
Email: m.linckelmann@abdn.ac.uk

Michał Stolorz
Affiliation: Department of Mathematical Sciences, University of Aberdeen, Aberdeen, AB24 3FX Scotland, United Kingdom
Email: ro2mjs8@abdn.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2012-11381-4
Received by editor(s): April 26, 2011
Published electronically: March 8, 2012
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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