Higher preprojective algebras and stably Calabi-Yau properties

TL;DR

This paper characterizes higher preprojective algebras through homological properties involving Gorenstein conditions and bimodule isomorphisms, establishing criteria for their identification.

Contribution

It provides sufficient and necessary homological conditions for finite dimensional graded algebras to be higher preprojective algebras, extending existing characterizations.

Findings

Identifies homological properties characterizing higher preprojective algebras

Proves these properties are necessary for 3-preprojective algebras

Extends results to higher representation finite algebras

Abstract

In this paper, we give sufficient properties for a finite dimensional graded algebra to be a higher preprojective algebra. These properties are of homological nature, they use Gorensteiness and bimodule isomorphisms in the stable category of Cohen-Macaulay modules. We prove that these properties are also necessary for $3$-preprojective algebras using \cite{Kel11} and for preprojective algebras of higher representation finite algebras using \cite{Dugas}.