Socle deformed preprojective algebras of generalized Dynkin type

TL;DR

This paper classifies finite-dimensional self-injective algebras socle equivalent to preprojective algebras of generalized Dynkin type, showing they are deformed preprojective algebras and periodic.

Contribution

It provides a complete classification and demonstrates that these algebras are deformed preprojective algebras of generalized Dynkin type.

Findings

Algebras are deformed preprojective of generalized Dynkin type

All such algebras are periodic

Classification is complete and explicit

Abstract

We provide a complete classification of finite-dimensional self-injective algebras which are socle equivalent to preprojective algebras of generalized Dynkin type. In particular, we conclude that these algebras are deformed preprojective algebras of generalized Dynkin type (in the sense of [5, 12]), and hence are periodic algebras.