On Generalized Cluster Categories

Claire Amiot (1)

1 IRMA - Institut de Recherche Mathématique Avancée

Cluster categories have been introduced by Buan, Marsh, Reineke, Reiten and Todorov in order to categorify Fomin-Zelevinsky cluster algebras. This survey motivates and outlines the construction of a generalization of cluster categories, and explains different applications of these new categories in representation theory.

Mots clés: preprojective algebras; cluster categories; 2-Calabi-Yau triangulated categories; cluster-tilting theory; quiver mutation; quivers with potentials; Jacobian algebras; preprojective algebras.

Domaines: Théorie des représentations [math.RT]

Claire Amiot. On Generalized Cluster Categories. 2011. ⟨hal-00557532v2⟩