JournalscmhVol. 81, No. 3pp. 595–616

Cluster algebras as Hall algebras of quiver representations

  • Philippe Caldero

    Université Claude Bernard Lyon 1, Villeurbanne, France
  • Frédéric Chapoton

    Université de Strasbourg, France
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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 A-D-E can be recovered from the data of the corresponding quiver representation category. This also provides some explicit formulas for cluster variables.

Cite this article

Philippe Caldero, Frédéric Chapoton, Cluster algebras as Hall algebras of quiver representations. Comment. Math. Helv. 81 (2006), no. 3, pp. 595–616

DOI 10.4171/CMH/65