Cluster-Tilted Algebras and Their Intermediate Coverings

DOI10.1080/00927872.2010.489082zbMath1250.16015arXiv0808.2352OpenAlexW2963464352MaRDI QIDQ3092961

Bin Zhu

Publication date: 12 October 2011

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

Full work available at URL: https://arxiv.org/abs/0808.2352

zbMATH Keywords

triangulated categoriesAuslander-Reiten translationsGalois coveringscluster-tilted algebrascluster algebrasbounded derived categoriescluster categoriesorbit categoriesintermediate coverings

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60) Derived categories and associative algebras (16E35)

Related Items

Relative cluster tilting objects in triangulated categories ⋮ On cluster-tilting objects in a triangulated category with Serre duality ⋮ Hall polynomials for representation-finite repetitive cluster-tilted algebras. ⋮ REPETITIVE HIGHER CLUSTER CATEGORIES OF TYPE A_n ⋮ Grothendieck groups in extriangulated categories ⋮ The dimension vectors of indecomposable modules of cluster-tilted algebras and the Fomin-Zelevinsky denominators conjecture. ⋮ On cluster-tilting graphs for hereditary categories ⋮ On Lie algebras associated with representation-finite algebras. ⋮ Triangulated categories with cluster tilting subcategories ⋮ Finite Repetitive Generalized Cluster Complexes and d-Cluster Categories ⋮ Repetitive cluster categories of type \(D_n\) ⋮ Combinatorial model for the cluster categories of type \(E\)

Cites Work

• Unnamed Item
• Unnamed Item
• Cluster-concealed algebras.
• Tame algebras and integral quadratic forms
• From iterated tilted algebras to cluster-tilted algebras.
• Equivalences between cluster categories
• Cluster-tilted algebras of finite representation type.
• Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
• Auslander correspondence.
• Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
• Cluster-tilted algebras and slices.
• The self-injective cluster-tilted algebras.
• On the Galois coverings of a cluster-tilted algebra.
• Preprojective modules over Artin algebras
• Covering spaces in representation-theory
• Perpendicular categories with applications to representations and sheaves
• Cluster mutation via quiver representations.
• From triangulated categories to abelian categories: cluster tilting in a general framework
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• From triangulated categories to cluster algebras
• Tilting theory and cluster combinatorics.
• Cluster algebras I: Foundations
• Cluster algebras, quiver representations and triangulated categories
• Cluster-tilted algebras
• From triangulated categories to cluster algebras II
• The cluster category of a canonical algebra
• Generalized associahedra via quiver representations
• Tilting in abelian categories and quasitilted algebras
• Cluster-tilted algebras as trivial extensions
• Quivers with relations arising from clusters (𝐴_{𝑛} case)
• A characterization of hereditary categories with tilting object