Classification of variants of partial Brauer monoids

Ivana Đurđev Brković

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