2006/12/22 by Claude Cibils, Pu Zhang, Cibils, Claude +1
Mathematics · #18E30 16G10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT #msc:16G10 #msc:18E30
paper · pdf · doi:10.48550/arxiv.math/0612689
18 pages
arxiv created 2006/12/22 · openalex publication_date 2006/12/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 this way the self-injective Nakayama algebras admitting indecomposable CY modules. In particular, this result recovers the algebras whose stable categories are Calabi-Yau, which have been obtained in [BS].