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arXiv · 1811.09060

Gr\"obner basis and the automaton property of Hecke--Kiselman algebras

Arkadiusz Mȩcel·Jan Okniński
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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 Gr\"obner basis.

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Arkadiusz Mȩcel, Jan Okniński. 2018-11-22. Gr\"obner basis and the automaton property of Hecke--Kiselman algebras. https://arxiv.org/abs/1811.09060

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