Mathematical Research Letters
Volume 21 (2014)
Higher preprojective algebras and stably Calabi-Yau properties
Pages: 617 – 647
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  and for preprojective algebras of higher representation finite algebras using .
Cohen-Macaulay modules, stable categories, Calabi-Yau categories, preprojective algebras, Calabi-Yau algebras
2010 Mathematics Subject Classification
16E05, 16E35, 16E65, 16G50, 18E30