Algebras of acyclic cluster type: Tree type and typeÃ

DOI10.1215/00277630-2083124zbMath1304.16011arXiv1009.4065OpenAlexW3121322109MaRDI QIDQ2843351

Claire Amiot, Steffen Oppermann

Publication date: 22 August 2013

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.4065

zbMATH Keywords

derived equivalencespath algebrastreescluster-tilted algebrasbounded derived categoriescluster categoriesgeneralized cluster categoriesglobal dimension 2tree-cluster types

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Graded rings and modules (associative rings and algebras) (16W50) Homological dimension in associative algebras (16E10) Cluster algebras (13F60) Derived categories and associative algebras (16E35)

Related Items (8)

Derived invariants for surface algebras ⋮ The derived category of surface algebras: the case of the torus with one boundary component ⋮ Quipu quivers and Nakayama algebras with almost separate relations ⋮ Algebras from surfaces without punctures ⋮ Derived equivalence of surface algebras in genus 0 via graded equivalence. ⋮ \(d\)-representation-finite self-injective algebras ⋮ Derived invariants for surface cut algebras of global dimension 2 II: the punctured case ⋮ Morita theorem for hereditary Calabi-Yau categories

Uses Software

• quivermutation

Cites Work

• Unnamed Item
• Mutation classes of \(\widetilde A_n\)-quivers and derived equivalence classification of cluster tilted algebras of type \(\widetilde A_n\).
• On the derived category of a finite-dimensional algebra
• Derived equivalences from mutations of quivers with potential
• The cluster complex of an hereditary Artin algebra.
• Cluster categories for algebras of global dimension 2 and quivers with potential.
• Derived equivalence classification for cluster-tilted algebras of type \(A_n\).
• Quivers with potentials and their representations. I: Mutations.
• Iterated tilted algebras of type \({\tilde {\mathbb A}}_ n\)
• Cluster equivalence and graded derived equivalence.
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Tilting theory and cluster combinatorics.
• Making diagrams speak, in Bhāskara I's commentary on the \textit{Āryabhaṭīya}
• On triangulated orbit categories
• Cluster algebras I: Foundations
• Deformed Calabi–Yau completions
• Mutation of cluster-tilting objects and potentials
• Cluster structures for 2-Calabi–Yau categories and unipotent groups
• Acyclic Calabi–Yau categories
• The Image of the Derived Category in the Cluster Category
• Tilted algebras of type A_n
• The algebras with discrete derived category.

This page was built for publication: Algebras of acyclic cluster type: Tree type and typeÃ