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Cell algebra structures on monoid and twisted monoid algebras

Authors
  • May, Robert D.
Type
Preprint
Publication Date
May 25, 2015
Submission Date
Jan 18, 2015
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.

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