In this paper, we give a characterization of digraphs Q, {pipe}Q{pipe}≤4 such that the associated Hecke-Kiselman monoids HQ are finite. In general, a necessary condition for HQ to be a finite monoid is that Q is acyclic and its Coxeter components are Dynkin diagrams. We show, by constructing examples, that such conditions are not sufficient. © 2012 Springer Science+Business Media, LLC.
Aragona R., D'Andrea A. (2013). Hecke-Kiselman monoids of small cardinality. SEMIGROUP FORUM, 86(1), 32-40 [10.1007/s00233-012-9422-2].
Hecke-Kiselman monoids of small cardinality
D'Andrea A.
2013
Abstract
In this paper, we give a characterization of digraphs Q, {pipe}Q{pipe}≤4 such that the associated Hecke-Kiselman monoids HQ are finite. In general, a necessary condition for HQ to be a finite monoid is that Q is acyclic and its Coxeter components are Dynkin diagrams. We show, by constructing examples, that such conditions are not sufficient. © 2012 Springer Science+Business Media, LLC.File in questo prodotto:
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