Hecke-Kiselman Monoids of Small Cardinality

Abstract

In this paper, we give a characterization of digraphs $Q,|Q|\le 4$ such that the associated Hecke-Kiselman monoid $H_Q$ is finite. In general, a necessary condition for $H_Q$ to be a finite monoid is that $Q$ is acyclic and its Coxeter components are Dynkin diagram. We show, by constructing examples, that such conditions are not sufficient.

Cited by in corpus (4)

• Combinatorics and structure of Hecke-Kiselman algebras
• Normal form in Hecke-Kiselman monoids associated with simple oriented graphs
• On the radical of a Hecke-Kiselman algebra
• A complete classification of endomorphisms of Kiselman's semigroup