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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 the cluster multiplication theorem for acyclic cluster algebras


Author: Fan Xu
Journal: Trans. Amer. Math. Soc. 362 (2010), 753-776
MSC (2000): Primary 16G20, 16G70; Secondary 14M99, 18E30
Published electronically: September 14, 2009
MathSciNet review: 2551505
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Abstract: Caldero and Keller, and Hubery have proved the cluster multiplication theorems for finite type and affine type. We generalize their results and prove the cluster multiplication theorem for arbitrary type using the 2-Calabi-Yau property and a property we call `higher order associativity'.


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Additional Information

Fan Xu
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
Email: fanxu@mail.tsinghua.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04946-0
PII: S 0002-9947(09)04946-0
Keywords: 2-Calabi-Yau, cluster category
Received by editor(s): November 15, 2007
Published electronically: September 14, 2009
Additional Notes: This research was partially supported by the NSF of China (No. 10631010)
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.