Maximal rigid subcategories in 2-Calabi-Yau triangulated categories.

DOI10.1016/j.jalgebra.2011.09.027zbMath1248.16013arXiv1004.5475OpenAlexW2963201008MaRDI QIDQ411750

Yu Zhou, Bin Zhu

Publication date: 30 April 2012

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

Full work available at URL: https://arxiv.org/abs/1004.5475

zbMATH Keywords

endomorphism algebrasGorenstein algebrasrepresentation types2-CY triangulated categoriescluster tilting subcategoriesmaximal rigid subcategories

Mathematics Subject Classification ID

Related Items (35)

Green groupoids of 2-Calabi–Yau categories, derived Picard actions, and hyperplane arrangements ⋮ On rooted cluster morphisms and cluster structures in 2-Calabi-Yau triangulated categories ⋮ Relative rigid objects in triangulated categories ⋮ The Grothendieck groups and stable equivalences of mesh algebras ⋮ Relative cluster tilting objects in triangulated categories ⋮ Two-term relative cluster tilting subcategories, \(\tau\)-tilting modules and silting subcategories ⋮ Mutation of torsion pairs in triangulated categories and its geometric realization ⋮ Cluster algebras arising from cluster tubes I: integer vectors ⋮ Relative Oppermann-Thomas cluster tilting objects in \((n+2)\)-angulated categories ⋮ Cluster structures in 2-Calabi-Yau triangulated categories of Dynkin type with maximal rigid objects ⋮ Algebras of finite representation type arising from maximal rigid objects ⋮ Relative rigid subcategories and \(\tau\)-tilting theory ⋮ Introduction to τ-tilting theory ⋮ Derived equivalences of self‐injective 2‐Calabi–Yau tilted algebras ⋮ Cotorsion pairs in cluster categories of type \(A_\infty^\infty\) ⋮ On the finiteness of the derived equivalence classes of some stable endomorphism rings ⋮ Lifting to two-term relative maximal rigid subcategories in triangulated categories ⋮ On cluster-tilting objects in a triangulated category with Serre duality ⋮ Torsion pairs in finite 2-Calabi-Yau triangulated categories with maximal rigid objects ⋮ Maximal rigid subcategories and cluster-tilting subcategories in 2-CY categories ⋮ Endomorphism Algebras of Maximal Rigid Objects in Cluster Tubes ⋮ -tilting theory ⋮ Homological classification of 4d \(\mathcal{N} = 2\) QFT. Rank-1 revisited ⋮ Auslander-Reiten Sequences or Triangles Related to Rigid Subcategories ⋮ Maximal \(\tau_d\)-rigid pairs ⋮ Relative homology, higher cluster-tilting theory and categorified Auslander-Iyama correspondence ⋮ On support \(\tau\)-tilting modules over endomorphism algebras of rigid objects ⋮ Triangulated categories with cluster tilting subcategories ⋮ Maximal rigid objects without loops in connected 2-CY categories are cluster-tilting objects ⋮ Cluster algebras arising from cluster tubes ⋮ Lifting to maximal rigid objects in 2-Calabi-Yau triangulated categories ⋮ Cluster algebras arising from cluster tubes. II: the Caldero-Chapoton map ⋮ Unnamed Item ⋮ Support \(\tau_n\)-tilting pairs ⋮ On Modules over Endomorphism Algebras of Maximal Rigid Objects in 2-Calabi-Yau Triangulated Categories

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