Classification of variants of partial Brauer monoids

Abstract

A variant of a semigroup $S$ with respect to an element $a\in S$ is the semigroup $S^a=(S,{\star }_a)$, where $x{\star }_{a}y=xay$ for any $x,y\in S$. Here, $a$ is the sandwich element of $S^a$. In this article, we study variants of the partial Brauer monoid ${\mathcal{P}\mathcal{B}}_n$ for $n\in \mathbb{N}$. We give the classification of these variants in the case when the rank of the sandwich element is nonzero.

12 pages, 7 figures

References in corpus (4)

• Transformation Semigroups with the Deformed Multiplication
• Green's relations on the deformed transformation semigroups
• Sandwich semigroups in diagram categories
• Deformed multiplication in the semigroup PT_n