Relative cluster tilting objects in triangulated categories

DOI10.1090/tran/7242zbMath1456.16011arXiv1504.00093OpenAlexW2605101196MaRDI QIDQ4561803

Bin Zhu, Wuzhong Yang

Publication date: 13 December 2018

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.00093

zbMATH Keywords

mutationscluster-tilting objectssupport \(\tau\)-tilting modulesrelative cluster tilting objects

Mathematics Subject Classification ID

Torsion theories, radicals (18E40) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Bimodules in associative algebras (16D20) Relative homological algebra, projective classes (category-theoretic aspects) (18G25)

Related Items (11)

Relative rigid objects in triangulated categories ⋮ Two-term relative cluster tilting subcategories, \(\tau\)-tilting modules and silting subcategories ⋮ Relative Oppermann-Thomas cluster tilting objects in \((n+2)\)-angulated categories ⋮ Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors ⋮ Relative rigid subcategories and \(\tau\)-tilting theory ⋮ Lifting to two-term relative maximal rigid subcategories in triangulated categories ⋮ Relative n-rigid objects in (n + 2)-angulated categories ⋮ Triangulated categories with cluster tilting subcategories ⋮ Relative rigid objects in extriangulated categories ⋮ Support \(\tau_n\)-tilting pairs ⋮ Support $\tau $-tilting modules and recollements

Cites Work

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• Rigid objects, triangulated subfactors and abelian localizations
• Maximal rigid subcategories in 2-Calabi-Yau triangulated categories.
• Projective dimension of modules over cluster-tilted algebras.
• On support \(\tau\)-tilting modules over endomorphism algebras of rigid objects
• Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
• Cluster characters for 2-Calabi-Yau triangulated categories.
• On the relation between cluster and classical tilting.
• From triangulated categories to abelian categories: cluster tilting in a general framework
• Generalized cluster complexes via quiver representations.
• Defining an \(m\)-cluster category.
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Tilting theory and cluster combinatorics.
• Rigid modules over preprojective algebras.
• On triangulated orbit categories
• On tilting modules over cluster-tilted algebras.
• Noetherian hereditary abelian categories satisfying Serre duality
• Cluster algebras I: Foundations
• On cluster-tilting objects in a triangulated category with Serre duality
• Cluster-Tilted Algebras and Their Intermediate Coverings
• Cluster structures for 2-Calabi–Yau categories and unipotent groups
• Lifting to Cluster-Tilting Objects in 2-Calabi–Yau Triangulated Categories
• Cluster-tilted algebras
• REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS
• Preprojective algebras and cluster algebras
• Torsion Theories and Tilting Modules
• Tilting Modules and Torsion Theories
• Generalized associahedra via quiver representations
• -tilting theory
• Quivers with relations arising from clusters (𝐴_{𝑛} case)

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