Classification of variants of partial Brauer monoids

Abstract

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