Torsion pairs and rigid objects in tubes.

DOI10.1007/s10468-013-9410-6zbMath1344.16013arXiv1112.6132OpenAlexW3103103880WikidataQ56285864 ScholiaQ56285864MaRDI QIDQ2015197

Karin Baur, Aslak Bakke Buan, Bethany R. Marsh

Publication date: 23 June 2014

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.6132

zbMATH Keywords

torsion theoriesAuslander-Reiten quiversannulusinverse limitstame hereditary algebrasPrüfer modulestorsion pairsdirect limitsmaximal rigid objectsadic modulesarc modeltube categories

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Torsion theories, radicals (18E40) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60)

Related Items (13)

Torsion pairs and cosilting in type \(\tilde{A}\) ⋮ A Geometric Model for the Module Category of a Gentle Algebra ⋮ Stability approach to torsion pairs on abelian categories ⋮ A geometric interpretation of categories of type \(\tilde{a}\) and of morphisms in the infinite radical ⋮ Compactifying exchange graphs. I: Annuli and tubes ⋮ Transfinite mutations in the completed infinity-gon ⋮ Torsion pairs in a triangulated category generated by a spherical object ⋮ Cotilting sheaves over weighted noncommutative regular projective curves ⋮ Cotorsion pairs in the cluster category of a marked surface ⋮ Torsion pairs in finite 2-Calabi-Yau triangulated categories with maximal rigid objects ⋮ Torsion pairs in cluster tubes ⋮ Large tilting sheaves over weighted noncommutative regular projective curves ⋮ The classification of \(\tau\)-tilting modules over Nakayama algebras

Cites Work

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• General heart construction on a triangulated category. I: Unifying \(t\)-structures and cluster tilting subcategories
• Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type \(A _{n }\)
• On the cluster category of a marked surface without punctures.
• Ext and inverse limits.
• Mutation of torsion pairs in triangulated categories and its geometric realization
• Tilting and cotilting for quivers of type \(\widetilde A_n\).
• Cotilting modules over tame hereditary algebras.
• A geometric model of tube categories.
• Torsion pairs in cluster tubes
• From triangulated categories to abelian categories: cluster tilting in a general framework
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Tilting in Grothendieck categories
• APPLICATIONS OF COTORSION PAIRS
• A Torsion Theory for Abelian Categories
• Homological and homotopical aspects of torsion theories

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