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On Generalized Cluster Categories
Claire Amiot1

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.
1:  IRMA - Institut de Recherche Mathématique Avancée
cluster categories – 2-Calabi-Yau triangulated categories – cluster-tilting theory – quiver mutation – quivers with potentials – Jacobian algebras – preprojective algebras.