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

2018/11/22 by Arkadiusz Mȩcel, Mȩcel, Arkadiusz, Jan Okniński +1 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1811.09060

openalex publication_date 2018/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Homogeneous finitely presented monoids of linear growth

Cited by

• A complete classification of endomorphisms of Kiselman's semigroup

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