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Cluster algebras as Hall algebras of quiver representations

Philippe Caldero·Frederic Chapoton
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Abstract

Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type ADE can be recovered from the data of the corresponding quiver representation category. This also provides some explicit formulas for cluster variables.

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Philippe Caldero, Frederic Chapoton. 2005-04-26. Cluster algebras as Hall algebras of quiver representations. https://arxiv.org/abs/math/0410187

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