The algebra of the monoid of orderpreserving functions on an $n$set and other reduced $E$Fountain semigroups
Abstract
With every reduced $E$Fountain semigroup $S$ which satisfies the generalized right ample condition we associate a category with partial composition $\mathcal{C}(S)$. Under some assumptions we prove an isomorphism of $\Bbbk$algebras $\Bbbk S\simeq\Bbbk\mathcal{C}(S)$ between the semigroup algebra and the category algebra where $\Bbbk$ is any commutative unital ring. This is a simultaneous generalization of a former result of the author on reduced EFountain semigroups which satisfy the congruence condition, a result of Junying Guo and Xiaojiang Guo on strict right ample semigroups and a result of Benjamin Steinberg on idempotent semigroups with central idempotents. The applicability of the new isomorphism is demonstrated with two wellknown monoids which are not members of the above classes. The monoid $\mathcal{O}_{n}$ of orderpreserving functions on an $n$set and the monoid of binary relations with demonic composition.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.08075
 arXiv:
 arXiv:2404.08075
 Bibcode:
 2024arXiv240408075S
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Group Theory;
 20M25;
 20M20;
 20M30;
 16G10
 EPrint:
 24 pages