Algebras of acyclic cluster type: tree type and type $\widetilde{A}$ - Archive ouverte HAL
Article Dans Une Revue Nagoya Mathematical Journal Année : 2016

Algebras of acyclic cluster type: tree type and type $\widetilde{A}$

Résumé

In this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of type $\widetilde{A}$. We are particularly interested in their derived equivalence classification. We prove that each algebra which is cluster equivalent to a tree quiver is derived equivalent to the path algebra of this tree. Then we describe explicitly the algebras of cluster type $\A_n$ for each possible orientation of $\A_n$. We give an explicit way to read off in which derived equivalence class such an algebra lies, and describe the Auslander-Reiten quiver of its derived category. Together, these results in particular provide a complete classification of algebras which are cluster equivalent to tame acyclic quivers.
Fichier principal
Vignette du fichier
clustertypeAv3.pdf (419.01 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00519712 , version 1 (21-09-2010)
hal-00519712 , version 2 (09-03-2012)

Identifiants

Citer

Claire Amiot, Steffen Oppermann. Algebras of acyclic cluster type: tree type and type $\widetilde{A}$. Nagoya Mathematical Journal, 2016, 211, pp.1-50. ⟨10.1017/S0027763000010771⟩. ⟨hal-00519712v2⟩
156 Consultations
108 Téléchargements

Altmetric

Partager

More