Cell algebra structures on monoid and twisted monoid algebras
Abstract
In this paper we study finite monoids M such that the group algebras over a domain R for all Schutzenberger groups of M are cell algebras. We show that for any such M the monoid algebra A over R has a standard cell algebra structure. Using properties of cell algebras we then find conditions for A to be quasi-hereditary and we show that if such an M is an inverse semi-group and R is a field k, then A is semi-simple if and only if the group algebras over k for all maximal subgroups of M are semi-simple. Finally, we show that for any "compatible" twisting of M into R the twisted monoid algebra is also a cell algebra and can thus be analyzed using cell algebra properties.
Cite
@article{arxiv.1501.04334,
title = {Cell algebra structures on monoid and twisted monoid algebras},
author = {Robert D. May},
journal= {arXiv preprint arXiv:1501.04334},
year = {2015}
}
Comments
17 pages, additional references added showing relations to previously known results, acknowledge that cell algebras coincide with the standardly based algebras previously introduced by Du and Rui