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2006•arXiv (Cornell University)Open access

Laurent expansions in cluster algebras via quiver representations

Philippe Caldero, Andrei V. Zelevinsky

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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.

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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.

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Available 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 concepts: Quiver, Cluster algebra, Mathematics, Cluster (spacecraft), Laurent polynomial, Laurent series, Pure mathematics, Algebra over a field

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