N-recollements and Virtually Gorenstein Algebras

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 $n\ge 2$, then $A$ is virtually Gorenstein if and only if so are $B$ and $C$.