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Mosc. Math. J., 2006, Volume 6, Number 3, Pages 411–429 (Mi mmj254)  

This article is cited in 45 scientific papers (total in 45 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

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.


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MSC: Primary 16G20; Secondary 14M15, 16S99
Received: April 6, 2004; in revised form May 1, 2006

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
\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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