Representations of Algebras and Related Topics

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pp: 1–53

DOI: 10.4171/101-1/1

On generalized cluster categories

Claire Amiot[1]

(1) Université de Strasbourg, France

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.

Keywords: Cluster categories, 2-Calabi-Yau triangulated categories, cluster-tilting theory, quiver mutation, quivers with potentials, Jacobian algebras, preprojective algebras