Combinatorics and structure of Hecke-Kiselman algebras

2019/04/27 by Jan Okniński, Magdalena Wiertel · 1 citation
Mathematics · #math.CO #math.RA #msc:05C25 #msc:16P40 #msc:16S15 #msc:16S36 #msc:20C08 #msc:20M05 #msc:20M25

paper · pdf · doi:10.1142/s0219199720500224

29 pages

arxiv created 2019/04/27 · arxiv updated 2020/06/02

Abstract

Hecke-Kiselman monoids \textrmHK_Θ and their algebras K[\textrmHK_Θ], over a field K, associated to finite oriented graphs Θ are studied. In the case Θ is a cycle of length n\geqslant 3, a hierarchy of certain unexpected structures of matrix type is discovered within the monoid C_n=\textrmHK_Θ and it is used to describe the structure and the properties of the algebra K[C_n]. In particular, it is shown that K[C_n] is a right and left Noetherian algebra, while it has been known that it is a PI-algebra of Gelfand-Kirillov dimension one. This is used to characterize all Noetherian algebras K[\textrmHK_Θ] in terms of the graphs Θ. The strategy of our approach is based on the crucial role played by submonoids of the form C_n in combinatorics and structure of arbitrary Hecke-Kiselman monoids \textrmHK_Θ.

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• Homomorphisms of Hecke-Kiselman Monoids Associated to Simple Oriented Graphs

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