Gröbner basis and the automaton property of Hecke--Kiselman algebras

Abstract

It is shown that the Hecke-Kiselman algebra associated to a finite directed graph is an automaton algebra in the sense of Ufnarovskii. Consequently, its Gelfand-Kirillov dimension is an integer if it is finite. As a consequence, it is proved that the Hecke-Kiselman algebra associated to an oriented cycle admits a finite Gröbner basis.

References in corpus (3)

• On Kiselman quotients of 0-Hecke monoids
• Quadratic automaton algebras and intermediate growth
• Homogeneous finitely presented monoids of linear growth