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Moscow Mathematical Journal, 2006, Volume 6, Number 3, Pages 411–429
DOI: https://doi.org/10.17323/1609-4514-2006-6-3-411-429 (Mi mmj254) 		 
This article is cited in 52 scientific papers (total in 52 papers)

Laurent expansions in cluster algebras via quiver representations

Ph. Calderoa, A. V. Zelevinskiib

a Institut Camille Jordan, Université Claude Bernard Lyon 1
b Northeastern University
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DOI: https://doi.org/10.17323/1609-4514-2006-6-3-411-429
Abstract: We study Laurent expansions of cluster variables in a cluster algebra of rank 2 associated to a generalized Kronecker quiver. In the case of the ordinary Kronecker quiver, we obtain explicit expressions for Laurent expansions of the elements of the canonical basis for the corresponding cluster algebra.
Key words and phrases: Cluster algebras, Laurent phenomenon, quiver representations, Kronecker quiver.
Received: April 6, 2004; in revised form May 1, 2006
Bibliographic databases:
MSC: Primary 16G20; Secondary 14M15, 16S99
Language: English
Citation: Ph. Caldero, A. V. Zelevinskii, “Laurent expansions in cluster algebras via quiver representations”, Mosc. Math. J., 6:3 (2006), 411–429
Citation in format AMSBIB
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\by Ph.~Caldero, A.~V.~Zelevinskii
\paper Laurent expansions in cluster algebras via quiver representations
\jour Mosc. Math.~J.
\yr 2006
\vol 6
\issue 3
\pages 411--429
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\crossref{https://doi.org/10.17323/1609-4514-2006-6-3-411-429}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2274858}
\zmath{https://zbmath.org/?q=an:1133.16012}
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