Cluster algebras as Hall algebras of quiver representations

@inproceedings{Caldero2006ClusterAA,
  title={Cluster algebras as Hall algebras of quiver representations},
  author={Philippe Caldero and Fr{\'e}d{\'e}ric Chapoton},
  year={2006}
}
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. Mathematics Subject Classification (2000). 16G20 16G70 18E30. 

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SHOWING 1-10 OF 16 REFERENCES

154 (2003)

  • S. Fomin, A. Zelevinsky, Cluster algebras. II. Finite type classification. Invent. Math
  • 63–121. Zbl
  • 1054
Highly Influential
5 Excerpts

36

  • M. Auslander, I. Reiten, S. O. Smalø, Representation theory of Artin algebras. Cambridge Stud. Adv. Math
  • Cambridge University Press, Cambridge
  • 1995
1 Excerpt

39

  • M. Demazure, P. Gabriel, Introduction to algebraic geometry, algebraic groups. Translated from the French by J. Bell, North-Holland Math. Stud
  • NorthHolland Publishing Co., Amsterdam
  • 1980

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