The structure of two generalization of the symmetric inverse semigroups

Abstract

We introduce two generalisations of the full symmetric inverse semigroup ${\mathcal{I}}_X$ and its dual semigroup ${{\mathcal{I}}^{\ast }}_X$ -- inverse semigroups ${{\mathcal{P}\mathcal{I}}^{\ast }}_X$ and ${\overline{{\mathcal{P}\mathcal{I}}^{\ast }}}_X$. Both of them have the same carrier and contain $\IS_X$. Binary operations on ${{\mathcal{P}\mathcal{I}}^{\ast }}_X$ and ${\overline{{\mathcal{P}\mathcal{I}}^{\ast }}}_X$ are reminiscent of the multiplication in ${\mathcal{I}}_X$. We use a convenient geometric way to realise elements from these two semigroups. This enables us to study efficiently their inner properties and to compare them with the corresponding properties of $\IS_X$ and ${{\mathcal{I}}^{\ast }}_X$.

24 pages

References in corpus (1)

• On presentations of Brauer-type monoids