Tilting modules arising from two-term tilting complexes

TL;DR

This paper demonstrates that two-term tilting complexes over Artin algebras induce tilting modules over factor algebras, linking derived equivalences between original and factor algebras.

Contribution

It establishes a connection between two-term tilting complexes and tilting modules over factor algebras, and describes the endomorphism algebra of these modules.

Findings

Every two-term tilting complex yields a tilting module over a factor algebra.

The endomorphism algebra of this tilting module is a specific factor algebra.

Derived equivalences via two-term tilting complexes extend to factor algebras.

Abstract

We show that every two-term tilting complex over an Artin algebra has a tilting module over a certain factor algebra as a homology group. Also, we determine the endomorphism algebra of such a homology group, which is given as a certain factor algebra of the endomorphism algebra of the two-term tilting complex. Thus, every derived equivalence between Artin algebras given by a two-term tilting complex induces a derived equivalence between the corresponding factor algebras.