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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Changjian Fu and Bernhard Keller
Journal: Trans. Amer. Math. Soc. 362 (2010), 859-895
MSC (2000): Primary 18E30, 16D90, 18G10
Published electronically: September 18, 2009
MathSciNet review: 2551509
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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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Additional Information

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: http://dx.doi.org/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
Published electronically: September 18, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.