Thick subcategories and virtually Gorenstein algebras

摘要

An Artin algebra is by definition virtually Gorenstein if the class ofmodules which are right orthogonal (with respect to Ext^*(-,-)) to allGorenstein projective modules coincides with the class of modules which areleft orthogonal to all Gorenstein injective modules. We provide a newcharacterization in terms of finitely generated modules. In addition, anexample of an algebra is presented which is not virtually Gorenstein.