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

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

2007-10-16

arxiv.org/abs/0710.3152v4

Mathematics

Representation Theory

35 pages, section 2 added, readability improved, references updated, to appear in Trans. AMS

Scientific paper

Building on work by Geiss-Leclerc-Schroer 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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