On the cluster multiplication theorem for acyclic cluster algebras

Xu, Fan

doi:10.1090/S0002-9947-09-04946-0

On the cluster multiplication theorem for acyclic cluster algebras
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by Fan Xu

Trans. Amer. Math. Soc. 362 (2010), 753-776

DOI: https://doi.org/10.1090/S0002-9947-09-04946-0

Published electronically: September 14, 2009

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Abstract:

Caldero and Keller, and Hubery have proved the cluster multiplication theorems for finite type and affine type. We generalize their results and prove the cluster multiplication theorem for arbitrary type using the 2–Calabi–Yau property and a property we call ‘higher order associativity’.

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