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Higher preprojective algebras and stably Calabi-Yau properties (1307.5828v2)
Published 22 Jul 2013 in math.RT
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}.