On Generalized Cluster Categories

Abstract

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.

survey 54pages, v2: small improvements, published in the proceedings of ICRA XIV "Representations of Algebras and Related Topics", European Mathematical Society

References in corpus (4)

• On triangulated orbit categories
• Calabi-Yau algebras
• Stable categories of Cohen-Macaulay modules and cluster categories
• Superpotential algebras and manifolds

Cited by in corpus (7)

• The representation type of Jacobian algebras
• Relative singularity categories I: Auslander resolutions
• Quivers with potentials associated to triangulated surfaces, Part III: tagged triangulations and cluster monomials
• Derived invariants for surface cut algebras II: the punctured case
• Relative Singularity Categories
• Categorical dynamical systems arising from sign-stable mutation loops
• Cyclic posets and triangulation clusters