Endomorphisms of Hecke-Kiselman Monoids Associated to Simple Oriented Graphs

TL;DR

This paper characterizes the endomorphism monoid of Hecke-Kiselman monoids associated with simple oriented graphs by presenting an isomorphic Boolean matrix monoid.

Contribution

It introduces a Boolean matrix monoid that is isomorphic to the endomorphism monoid of Hecke-Kiselman monoids, providing a new algebraic perspective.

Findings

The endomorphism monoid of $ ext{HK}_ heta$ is isomorphic to a Boolean matrix monoid.

Provides an explicit algebraic structure for endomorphisms of Hecke-Kiselman monoids.

Establishes a connection between graph-based monoids and Boolean matrix monoids.

Abstract

Let $\mathrm{HK}_{\Theta}$ denote the Hecke-Kiselman monoid associated to a finite simple oriented graph $\Theta$. We present a Boolean matrix monoid that is isomorphic to the endomorphism monoid $\mathrm{End}(\mathrm{HK}_{\Theta})$.