Transactions of the American Mathematical Society

Author(s): Changjian Fu; Bernhard Keller
Journal: Trans. Amer. Math. Soc. 362 (2010), 859-895.
MSC (2000): Primary 18E30, 16D90, 18G10
Posted: September 18, 2009
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 18E30, 16D90, 18G10

Changjian Fu
Affiliation: Department of Mathematics, Sichuan University, 610064 Chengdu, People's Republic of China
Email: flyinudream@yahoo.com.cn

Bernhard Keller
Affiliation: U.F.R. de Mathématiques, Institut de Mathématiques, U.M.R. 7586 du CNRS, Université Paris Diderot - Paris 7, Case 7012, Bâtiment Chevaleret, 75205 Paris Cedex 13, France
Email: keller@math.jussieu.fr

DOI: 10.1090/S0002-9947-09-04979-4
PII: S 0002-9947(09)04979-4
Keywords: Cluster algebra, tilting, 2-Calabi-Yau category
Received by editor(s): January 15, 2008
Posted: September 18, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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