Ph. Caldero, A. V. Zelevinskii, “Laurent expansions in cluster algebras via quiver representations”, Mosc. Math. J., 2006, Volume 6, Number 3,Pages <nobr>411

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Laurent expansions in cluster algebras via quiver representations

Ph. Caldero^a, A. V. Zelevinskii^b

^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.

MSC: Primary 16G20; Secondary 14M15, 16S99

Received: April 6, 2004; in revised form May 1, 2006

Language: English

DOI: 10.17323/1609-4514-2006-6-3-411-429