A pre-projective part of tilting quivers of certain path algebras

TL;DR

This paper investigates the structure of pre-projective tilting modules over certain path algebras, providing criteria for Ext-vanishing, a combinatorial characterization of their poset, and insights into the tilting quivers' structure.

Contribution

It introduces a criterion for Ext-vanishing in pre-projective modules and offers a new combinatorial description of the poset of basic pre-projective tilting modules.

Findings

Criterion for Ext-vanishing in pre-projective modules

Combinatorial characterization of the poset of tilting modules

Structural insights into the pre-projective part of tilting quivers

Abstract

D.Happel and L.Unger defined a partial order on the set of basic tilting modules. We study the poset of basic pre-projective tilting modules over path algebra of infinite type. First we will give a criterion for Ext-vanishing for pre-projective modules. And by using this we will give a combinatorial characterization of the poset of basic pre-projective tilting modules. Finally we will see a structure of a pre-projective part of tilting quivers.