Virtual gorensteinness over group algebras

Abstract

Let γ be a finite group, and let A be any Artin algebra. It is shown that the group algebra Λγ is virtually Gorenstein if and only if ΛΓ' is virtually Gorenstein, for all elementary abelian subgroups Γ of Γ We also extend this result to cover the more general context. Precisely, assume that Γ is a group in Kropholler's hierarchy HS, Γ is a subgroup of Γ of finite index, and Ris any ring with identity. It is proved that, in certain circumstances, that RΓ is virtually Gorenstein if and only if RΓ' is so. © 2015 by Kyoto University.