Mathematical Research Letters

Volume 21 (2014)

Number 4

Higher preprojective algebras and stably Calabi-Yau properties

Pages: 617 – 647



Claire Amiot (Institut Fourier, Université Joseph Fourier, Saint Martin d’Hères, France)

Steffen Oppermann (Institutt for matematiske fag, NTNU, Trondheim, Norway)


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


Cohen-Macaulay modules, stable categories, Calabi-Yau categories, preprojective algebras, Calabi-Yau algebras

2010 Mathematics Subject Classification

16E05, 16E35, 16E65, 16G50, 18E30

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