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ON KISELMAN QUOTIENTS OF 0HECKE MONOIDS
"... Abstract. Combining the definition of 0Hecke monoids with that of Kiselman semigroups, we define what we call Kiselman quotients of 0Hecke monoids associated with simply laced Dynkin diagrams. We classify these monoids up to isomorphism, determine their idempotents and show that they are Jtrivial ..."
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Abstract. Combining the definition of 0Hecke monoids with that of Kiselman semigroups, we define what we call Kiselman quotients of 0Hecke monoids associated with simply laced Dynkin diagrams. We classify these monoids up to isomorphism, determine their idempotents and show that they are Jtrivial. 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 orderpreserving and orderdecreasing total transformations on a finite chain. This, in particular, implies a presentation for the latter monoid. Finally, we construct various representations of these monoids by matrices, total transformations and binary relations. 1. Definitions and description of the results Let Γ be a simply laced Dynkin diagram (or a disjoint union of simply laced Dynkin diagrams). Then the 0Hecke monoid HΓ associated with
EFFECTIVE DIMENSION OF FINITE SEMIGROUPS
"... Abstract. In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to numerous examples. 1. ..."
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Abstract. In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to numerous examples. 1.
CATEGORIFICATION OF THE CATALAN MONOID
"... We construct a finitary additive 2category whose Grothendieck ring is isomorphic to the semigroup algebra of the monoid of orderdecreasing and orderpreserving transformations of a finite chain. ..."
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We construct a finitary additive 2category whose Grothendieck ring is isomorphic to the semigroup algebra of the monoid of orderdecreasing and orderpreserving transformations of a finite chain.