Higher preprojective algebras and stably Calabi-Yau properties

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 3preprojective algebras using [18] and for preprojective algebras of higher representation finite algebras using [5].