Classification of variants of partial Brauer monoids

Abstract

A variant of a semigroup S with respect to an element a C S is the semigroup Sa = (S,*a), where x *a y = xay for any x,y C S. Here, a is the sandwich element of S“. In this article, we study variants of the partial Brauer monoid PBn for n C N. We give the classification of these variants in the case when the rank of the sandwich element is nonzero.