Lifting of recollements and Gorenstein projective modules

TL;DR

This paper studies how recollements involving Gorenstein-projective modules can be lifted through homological ring epimorphisms, providing new insights into the structure of Gorenstein derived categories and conditions for finite CM-type.

Contribution

It introduces methods to lift recollements in Gorenstein contexts and establishes criteria for upper triangular matrix algebras to have finite CM-type.

Findings

Recollements can be lifted via homological ring epimorphisms.

Conditions for upper triangular matrix algebras to be of finite CM-type.

Connections between Gorenstein derived categories and stable categories.

Abstract

In the paper, we investigate the lifting of recollements with respect to Gorenstein-projective modules. Specifically, a homological ring epimorphism can induce a lifting of the recollement of the stable category of finitely generated Gorenstein-projective modules; the recollement of the bounded Gorenstein derived categories of some upper triangular matrix algebras can be lifted to the homotopy category of Gorenstein-projective modules. As a byproduct, we give a sufficient and necessary condition on the upper triangular matrix algebra T_{n}(A) to be of finite CM-type for an algebra A of finite CM-type.