Cell algebra structures on monoid and twisted monoid algebras
arXiv:1501.04334
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.
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