Maximal rigid subcategories and cluster-tilting subcategories in 2-CY categories

DOI10.1016/J.JALGEBRA.2016.10.030zbMath1405.16025OpenAlexW2553422681MaRDI QIDQ502717

Jinde Xu, Baiyu Ouyang

Publication date: 6 January 2017

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2016.10.030

zbMATH Keywords

2-CY triangulated categoriesmaximal rigid subcategoriescluster-tilting subcategories

Mathematics Subject Classification ID

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

Cites Work

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• Maximal rigid subcategories in 2-Calabi-Yau triangulated categories.
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• Applications of contravariantly finite subcategories
• Cluster categories of type \({\mathbb {A}}_\infty ^\infty \) and triangulations of the infinite strip
• Cluster tilting for one-dimensional hypersurface singularities
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Tilting theory and cluster combinatorics.
• Rigid modules over preprojective algebras.
• Noetherian hereditary abelian categories satisfying Serre duality
• Cluster structures for 2-Calabi–Yau categories and unipotent groups
• Maximal rigid objects without loops in connected 2-CY categories are cluster-tilting objects
• T -structures and torsion pairs in a 2-Calabi-Yau triangulated category

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