Preprojective algebras and cluster algebras

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We use the representation theory of preprojective algebras to construct and study certain cluster algebras related to semisimple algebraic groups.

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n-Abelian and n-exact categories (2014, background): “In a parallel direction, 2-cluster-tilting subcategories of the module category of a preprojective algebra of Dynkin type, which has infinite global dimension, are central in Geiß-Leclerc-Schröer’s categorification of cluster algebras arising in Lie theory, see [22] and the references therein.”
Representations of Algebras and Related Topics (2011, background): “Π2(∆), which helped them to categorify certain cluster algebras. Further developments of this link between cluster algebras and preprojective algebras can be found in [47], [48], [50], [51] (see also [49] for an overview). On generalized cluster categories 15 Theorem 2.11 (Geiss-Leclerc-Schr¨oer [46”
The periodicity conjecture for pairs of Dynkin diagrams (2010, unknown): “, for example, the surveys [8], [30], [48], [62], [64].”
Total positivity and cluster algebras (2010, background): “Several survey/introductory papers dedicated to the subjects in the title, approached from various perspectives, have already appeared in the literature; see in particular [1, 5, 19, 25, 29, 34, 39, 43, 55, 56, 57].”