Finitary 2-categories associated with dual projection functors

TL;DR

This paper explores the structure of finitary 2-categories linked to dual projection functors in finite dimensional algebras, revealing connections to Hecke-Kiselman monoids and providing presentations for related bimodule monoids.

Contribution

It establishes a correspondence between dual projection functor monoids and Hecke-Kiselman monoids for certain quivers, and offers new presentations for subbimodule monoids.

Findings

The monoid generated by dual projection functors is isomorphic to the Hecke-Kiselman monoid for admissible tree quivers.

A presentation for the monoid of indecomposable subbimodules of the identity bimodule is provided.

The results include all Dynkin quivers of type A.

Abstract

We study finitary 2-categories associated to dual projection functors for finite dimensional associative algebras. In the case of path algebras of admissible tree quivers (which includes all Dynkin quivers of type A) we show that the monoid generated by dual projection functors is the Hecke-Kiselman monoid of the underlying quiver and also obtain a presentation for the monoid of indecomposable subbimodules of the identity bimodule.