Distributive lattices and the poset of pre-projective tilting modules

TL;DR

This paper investigates the structure of the poset of basic pre-projective tilting modules over infinite type path algebras, providing conditions for it to be a distributive lattice and characterizing when such lattices correspond to these modules.

Contribution

It establishes necessary and sufficient conditions for the poset to be a distributive lattice and for such lattices to be isomorphic to the poset of pre-projective tilting modules over infinite type path algebras.

Findings

The poset of pre-projective tilting modules is a distributive lattice under certain conditions.

Conditions are provided for when a distributive lattice corresponds to these tilting modules.

Characterization of the poset structure over infinite type path algebras.

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. We give an equivalent condition for that this poset is a distributive lattice. We also give an equivalent condition for that a distributive lattice is isomorphic to the poset of basic pre-projective tilting modules over a path algebra of representation infinite type.