On the cluster multiplication theorem for acyclic cluster algebras
Fan Xu
TL;DR
This paper generalizes the cluster multiplication theorem to all types of acyclic cluster algebras using advanced algebraic properties, extending previous finite and affine type results.
Contribution
It introduces a proof of the cluster multiplication theorem for arbitrary type acyclic cluster algebras leveraging 2-Calabi-Yau properties and high order associativity.
Findings
Proved the cluster multiplication theorem for arbitrary acyclic types.
Extended previous finite and affine type results to all types.
Utilized 2-Calabi-Yau properties and high order associativity in proofs.
Abstract
In \cite{CK2005} and \cite{Hubery2005}, 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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry