Thick subcategories and virtually Gorenstein algebras

Abstract

An Artin algebra is by definition virtually Gorenstein if the class of modules which are right orthogonal (with respect to $\operatorname {Ext}^*(-,-)$) to all Gorenstein projective modules coincides with the class of modules which are left orthogonal to all Gorenstein injective modules. We provide a new characterization in terms of finitely generated modules. In addition, an example of an algebra is presented which is not virtually Gorenstein.