Skew Group Algebras, (Fg) and Self-injective Rad-Cube-Zero Algebras

Abstract

We classify self-injective radical cube zero algebras with respect to whether they satisfy certain finite generation conditions sufficient to have a fruitful theory of support varieties defined via Hochschild cohomology in the vein of (Erdmann et al, 2004) and (Snashall and Solberg, 2004). Using skew group algebras and Linckelmann's notion of separable equivalence, we obtain results that complement the existing partial classification of (Said, 2015) and complete the classification begun in (Erdmann and Solberg, 2011) and (Said, 2015) up to assumptions on the characteristic of the field.