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

TL;DR

This paper classifies self-injective radical cube zero algebras based on their support variety properties via Hochschild cohomology, extending prior classifications with new results using skew group algebras and separable equivalence.

Contribution

It provides a comprehensive classification of these algebras concerning finite generation conditions, utilizing skew group algebras and separable equivalence methods.

Findings

Complete classification of self-injective radical cube zero algebras under certain conditions.

Identification of when these algebras satisfy finite generation conditions for support varieties.

Extension of previous classifications to broader cases with characteristic assumptions.

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.