Auslander-Reiten Sequences or Triangles Related to Rigid Subcategories

DOI10.1142/S100538671600002XzbMath1339.16021OpenAlexW2226939717MaRDI QIDQ2796956

Ming Lu

Publication date: 30 March 2016

Published in: Algebra Colloquium (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s100538671600002x

zbMATH Keywords

Auslander-Reiten translationsAuslander-Reiten sequencescluster categoriesrigid objectscluster-tilting subcategoriesAuslander-Reiten trianglesCalabi-Yau triangulated categoriesfunctorially finite rigid subcategories

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60)

Cites Work

• General heart construction on a triangulated category. I: Unifying \(t\)-structures and cluster tilting subcategories
• Maximal rigid subcategories in 2-Calabi-Yau triangulated categories.
• Periodicity of \(d\)-cluster-tilted algebras.
• From triangulated categories to abelian categories: cluster tilting in a general framework
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Cluster algebras I: Foundations
• From triangulated categories to module categories via localisation
• Cluster-tilted algebras
• Quivers with relations arising from clusters (𝐴_{𝑛} case)

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