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On simple modules over twisted finite category algebras

Linckelmann, M. and Stolorz, M. (2012). On simple modules over twisted finite category algebras. Proceedings of the American Mathematical Society, 140(11), pp. 3725-3737.

Abstract

The purpose of this note 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 Ponizovski˘i 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.

Publication Type: Article
Additional Information: First published in Proceedings of the American Mathematical Society in volume 140, number 11, 2012, published by the American Mathematical Society
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/1873
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