N-recollements and Virtually Gorenstein Algebras

TL;DR

This paper explores the relationship between n-recollements of stable categories of Gorenstein projective modules and the virtual Gorensteinness of finite-dimensional algebras, establishing conditions under which this property is preserved.

Contribution

It proves that for n-recollements with n≥2, the virtual Gorensteinness of an algebra is equivalent to that of the algebras it is related to via the recollement.

Findings

Virtual Gorensteinness is preserved under n-recollements for n≥2.

The paper establishes an if and only if condition relating the Gorenstein property among related algebras.

Provides a new perspective on the structure of Gorenstein projective modules in algebra relations.

Abstract

The relation between the $n$-recollements of stable categories of Gorenstein projective modules and the virtual Gorensteinness of algebras are investigated. Let $A,B$, and $C$ be finite dimensional algebras. We prove that if the stable category of Gorenstein projective $A$-modules admits a $n$-recollement relative to that of $B$ and $C$ with $n\geq 2$, then $A$ is virtually Gorenstein if and only if so are $B$ and $C$.