Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type \(D\).

DOI10.1016/j.jalgebra.2014.03.034zbMath1348.16011arXiv1012.4661OpenAlexW2089297708MaRDI QIDQ403116

Thorsten Holm, Sefi Ladkani, Janine Bastian

Publication date: 29 August 2014

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

Full work available at URL: https://arxiv.org/abs/1012.4661

zbMATH Keywords

Cartan matricesderived categoriesderived equivalencesfinite representation typeDynkin diagramstilting complexesCartan determinantscluster tilted algebrascluster tilting objectsgood mutationsquiver mutations

Mathematics Subject Classification ID

Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60) Derived categories and associative algebras (16E35)

Related Items

Minimal length maximal green sequences ⋮ Derived equivalences of self‐injective 2‐Calabi–Yau tilted algebras ⋮ Derived equivalence classification of the cluster-tilted algebras of Dynkin type \(E\). ⋮ Zavadskij modules over cluster-tilted algebras of type \(\mathbb{A}\) ⋮ Singularity categories of some 2-CY-tilted algebras ⋮ On mutations of selfinjective quivers with potential. ⋮ EXPLICIT CONSTRUCTION OF COMPANION BASES ⋮ A Course on Cluster Tilted Algebras ⋮ The singularity categories of the cluster-tilted algebras of Dynkin type.

Uses Software

• Magma
• quivermutation

Cites Work

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• Mutation classes of \(\widetilde A_n\)-quivers and derived equivalence classification of cluster tilted algebras of type \(\widetilde A_n\).
• Cluster-tilted algebras of finite representation type.
• Quivers with relations and cluster tilted algebras.
• Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
• Derived equivalence classification for cluster-tilted algebras of type \(A_n\).
• Gentle algebras arising from surface triangulations.
• The self-injective cluster-tilted algebras.
• Cluster algebras and triangulated surfaces. I: Cluster complexes
• The number of elements in the mutation class of a quiver of type \(D_n\).
• Quivers with potentials and their representations. I: Mutations.
• The derived equivalence classification of representation-finite selfinjective algebras
• The Magma algebra system. I: The user language
• Derived equivalence classification of the cluster-tilted algebras of Dynkin type \(E\).
• Equivalences of derived categories for selfinjective algebras.
• On derived equivalences of categories of sheaves over finite posets
• A geometric model for cluster categories of type \(D_n\).
• On the periodicity of Coxeter transformations and the non-negativity of their Euler forms
• Tilting theory and cluster combinatorics.
• Cartan determinants for gentle algebras.
• Cluster algebras I: Foundations
• Mutation of cluster-tilting objects and potentials
• Cluster-tilted algebras
• The Mutation Class ofD_nQuivers
• Quivers with potentials associated to triangulated surfaces
• Morita Theory for Derived Categories
• Weakly symmetric algebras of Euclidean type
• Quivers with relations arising from clusters (𝐴_{𝑛} case)