A note on a homological epimorphism whose source is a piecewise hereditary algebra

TL;DR

This paper investigates homological epimorphisms between proper dg algebras, demonstrating that when the source is a finite dimensional piecewise hereditary algebra, the target is derived equivalent to a piecewise hereditary algebra.

Contribution

It establishes a link between homological epimorphisms and derived equivalences in the context of piecewise hereditary algebras.

Findings

Target algebra is derived equivalent to a piecewise hereditary algebra

Homological epimorphism preserves certain derived properties

Results apply to finite dimensional proper dg algebras

Abstract

We study a homological epimorphism of proper dg algebras and show that if the source is a finite dimensional piecewise hereditary algebra, then the target is derived equivalent to some piecewise hereditary algebra.