Endomorphism algebras of semi-tilting modules

TL;DR

This paper studies the structure of endomorphism algebras of semi-tilting modules over finite-dimensional algebras and shows their relation to BB-tilting modules through mutations.

Contribution

It demonstrates that endomorphism algebras from mutations of semi-tilting modules can be realized as endomorphism algebras of BB-tilting modules.

Findings

Endomorphism algebras of semi-tilting modules are structurally related to BB-tilting modules.

Mutations of semi-tilting modules produce endomorphism algebras equivalent to those of BB-tilting modules.

Abstract

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$. We investigate the structure properties of the endomorphism algebras of semi-tilting $A$-modules, and prove that the endomorphism algebras arising from the mutations of semi-tilting $A$-modules can be realized as the endomorphism algebras of BB-tilting modules.