Cell algebra structures on monoid and twisted monoid algebras

Autor:	May, Robert D.
Rok vydání:	2015
Předmět:	Mathematics - Rings and Algebras 16S36 (primary) 20M25 20M30 (secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1501.04334 Zobrazit plný text záznamu View this record from Arxiv