ON KISELMAN QUOTIENTS OF 0-HECKE MONOIDS

Authors : Olexandr Ganyushkin, Volodymyr Mazorchuk

Pages : 174-191

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Publication Date : 2011-12-01

Article Type : Research Paper

Abstract :Combining the definition of 0-Hecke monoids with that of Kiselman semigroups, we define what we call Kiselman quotients of 0-Hecke monoids associated with simply laced Dynkin diagrams. We classify these monoids up to isomorphism, determine their idempotents and show that they are J -trivial. For type A we show that Catalan numbers appear as the maximal cardinality of our monoids, in which case the corresponding monoid is isomorphic to the monoid of all order-preserving and order-decreasing total transformations on a finite chain. We construct various representations of these monoids by matrices, total transformations and binary relations. Motivated by these results, with a mixed graph we associate a monoid, which we call a Hecke-Kiselman monoid, and classify such monoids up to isomorphism. Both Kiselman semigroups and Kiselman quotients of 0-Hecke monoids are natural examples of Hecke-Kiselman monoids.
Keywords : 0 Hecke monoid, Kiselman type semigroup, action, isomorphism