Open Access
2019 Growth alternative for Hecke-Kiselman monoids
Arkadiusz Meçel, Jan Okniński
Publ. Mat. 63(1): 219-240 (2019). DOI: 10.5565/PUBLMAT6311907


The Gelfand–Kirillov dimension of Hecke–Kiselman algebras defined by oriented graphs is studied. It is shown that the dimension is infinite if and only if the underlying graph contains two cycles connected by an (oriented) path. Moreover, in this case, the Hecke–Kiselman monoid contains a free noncommutative submonoid. The dimension is finite if and only if the monoid algebra satisfies a polynomial identity.


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Arkadiusz Meçel. Jan Okniński. "Growth alternative for Hecke-Kiselman monoids." Publ. Mat. 63 (1) 219 - 240, 2019.


Received: 5 May 2017; Revised: 8 January 2018; Published: 2019
First available in Project Euclid: 7 December 2018

zbMATH: 07040967
MathSciNet: MR3908792
Digital Object Identifier: 10.5565/PUBLMAT6311907

Primary: 16P90 , 16S15 , 16S36 , 16S99 , 20M05

Keywords: Gelfand–Kirillov dimension , growth alternative , Hecke–Kiselman monoid , oriented simple graph

Rights: Copyright © 2019 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.63 • No. 1 • 2019
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