Monoid algebras of projection functors

Details Monoid algebras of projection functors Monoid algebras of projection functors

2012-03-08

arxiv.org/abs/1203.1943v1

Mathematics

Representation Theory

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Scientific paper

We study the monoid of so called projection functors $\p{S}$ attached to simple modules $S$ of a finite dimensional algebra, which appear naturally in the study of torsion pairs. We determine defining relations in special cases of path algebras. For the linearly oriented Dynkin quiver of Type $A$, we get an isomorphism to the monoid of non-decreasing parking functions. Moreover we give an explicit isomorphism between the monoid algebra of non-decreasing parking functions and a certain incidence algebra independent of the field.

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