On the cluster multiplication theorem for acyclic cluster algebras

2007/11/21 by Fan Xu, Xu, Fan · 2 citations
Mathematics · #14M99 #16G20 #16G70 #18E30 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0711.3255

openalex publication_date 2007/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In \citeCK2005 and \citeHubery2005, the authors proved the cluster multiplication theorems for finite type and affine type. We generalize their results and prove the cluster multiplication theorem for arbitrary type by using the properties of 2--Calabi--Yau (Auslander--Reiten formula) and high order associativity.

Citations

• On triangulated orbit categories

Cited by

• Fundamental relations in quantum cluster algebras
• A module-theoretic interpretation of quantum expansion formula

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