Trends in Representation Theory of Algebras and Related Topics

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pp: 467–489

DOI: 10.4171/062-1/11

Calabi–Yau triangulated categories

Bernhard Keller[1]

(1) UFR de Mathématiques, Université Paris Diderot - Paris 7, Case 7012, Bâtiment Chevaleret, 75205, PARIS CEDEX 13, FRANCE

We review the definition of a Calabi–Yau triangulated category and survey examples coming from the representation theory of quivers and finite-dimensional algebras. Our main motivation comes from the links between quiver representations and Fomin–Zelevinsky’s cluster algebras.

Keywords: Triangulated category, Calabi–Yau category, cluster algebra