# Cell algebra structures on monoid and twisted monoid algebras

- Authors
- Type
- Preprint
- Publication Date
- Submission Date
- Identifiers
- arXiv ID: 1501.04334
- Source
- arXiv
- License
- Yellow
- External links

## 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.