Triangulated categories with cluster tilting subcategories

DOI10.2140/pjm.2019.301.703zbMath1454.16020arXiv1711.04290OpenAlexW3099712136WikidataQ126984589 ScholiaQ126984589MaRDI QIDQ2305361

Bin Zhu, Panyue Zhou, Wuzhong Yang

Publication date: 10 March 2020

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.04290

zbMATH Keywords

cluster tilting subcategoriestilting subcategories(support) \( \tau \)-tilting subcategoriesghost cluster 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) Representation theory of associative rings and algebras (16G99) Monoidal categories, symmetric monoidal categories (18M05)

Related Items (4)

Relative rigid objects in triangulated categories ⋮ Two-term relative cluster tilting subcategories, \(\tau\)-tilting modules and silting subcategories ⋮ Relative rigid subcategories and \(\tau\)-tilting theory ⋮ Support \(\tau_n\)-tilting pairs

Cites Work

• Rigid objects, triangulated subfactors and abelian localizations
• Maximal rigid subcategories in 2-Calabi-Yau triangulated categories.
• Projective dimension of modules over cluster-tilted algebras.
• Intermediate co-\(t\)-structures, two-term silting objects, \(\tau\)-tilting modules, and torsion classes
• On a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon
• On support \(\tau\)-tilting modules over endomorphism algebras of rigid objects
• Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
• Cotorsion pairs in cluster categories of type \(A_\infty^\infty\)
• Applications of contravariantly finite subcategories
• Cluster categories of type \({\mathbb {A}}_\infty ^\infty \) and triangulations of the infinite strip
• Continuous cluster categories. I
• From triangulated categories to abelian categories: cluster tilting in a general framework
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Tilting theory and cluster combinatorics.
• Cluster tilting subcategories and torsion pairs in Igusa-Todorov cluster categories of Dynkin type \(A_{ \infty }\)
• Triangulated Categories
• Noetherian hereditary abelian categories satisfying Serre duality
• Reduction of τ-Tilting Modules and Torsion Pairs
• 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 Categories Coming from Cyclic Posets
• Relative cluster tilting objects in triangulated categories
• Representation Theory of Artin Algebras I
• A Caldero–Chapoton map for infinite clusters
• -tilting theory

This page was built for publication: Triangulated categories with cluster tilting subcategories