On cluster algebras with coefficients and 2-Calabi-Yau categories

Fu, Changjian; Keller, Bernhard

doi:10.1090/S0002-9947-09-04979-4

On cluster algebras with coefficients and 2-Calabi-Yau categories
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by Changjian Fu and Bernhard Keller PDF

Trans. Amer. Math. Soc. 362 (2010), 859-895 Request permission

Abstract:

Building on work by Geiss-Leclerc-Schröer and by Buan-Iyama-Reiten-Scott we investigate the link between certain cluster algebras with coefficients and suitable 2-Calabi-Yau categories. These include the cluster categories associated with acyclic quivers and certain Frobenius subcategories of module categories over preprojective algebras. Our motivation comes from the conjectures formulated by Fomin and Zelevinsky in ‘Cluster algebras IV: Coefficients’. We provide new evidence for Conjectures 5.4, 6.10, 7.2, 7.10 and 7.12 and show by an example that the statement of Conjecture 7.17 does not always hold.

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