Cluster algebras as Hall algebras of quiver representations

Philippe Caldero, Frédéric Chapoton

Type: Article

Publication Date: 2006-09-30

Citations: 438

DOI: https://doi.org/10.4171/cmh/65

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.

Locations

Commentarii Mathematici Helvetici - View - PDF
arXiv (Cornell University) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF

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