Calabi-Yau objects in triangulated categories

Cibils, Claude; Zhang, Pu

doi:10.1090/S0002-9947-09-04682-0

Calabi-Yau objects in triangulated categories
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by Claude Cibils and Pu Zhang PDF

Trans. Amer. Math. Soc. 361 (2009), 6501-6519 Request permission

Abstract:

We introduce the Calabi-Yau (CY) objects in a Hom-finite Krull-Schmidt triangulated $k$-category, and notice that the structure of the minimal, consequently all the CY objects, can be described. The relation between indecomposable CY objects and Auslander-Reiten triangles is provided. Finally we classify all the CY modules of self-injective Nakayama algebras, determining in this way the self-injective Nakayama algebras admitting indecomposable CY modules.

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