Integral bases of cluster algebras and representations of tame quivers

Abstract

In \cite{CK2005} and \cite{SZ}, the authors constructed the bases of cluster algebras of finite types and of type ${\tilde{A}}_{1,1}$, respectively. In this paper, we will deduce $\mathbb{Z}$-bases for cluster algebras of affine types.

28 pages, an improvement of arXiv:0811.3676

References in corpus (5)

• Cluster algebra structures and semicanonical bases for unipotent groups
• Cluster characters II: A multiplication formula
• Comment on a recent conjectured solution of the three-dimensional Ising model arXiv:0705.1045
• Notes on the cluster multiplication formulas for 2-Calabi-Yau categories
• On the cluster multiplication theorem for acyclic cluster algebras

Cited by in corpus (6)

• Quiver varieties and cluster algebras
• Cluster algebras via cluster categories with infinite-dimensional morphism spaces
• Positivity for Regular Cluster Characters in Acyclic Cluster Algebras
• Bases of the quantum cluster algebra of the Kronecker quiver
• Multiplicative properties of a quantum Caldero-Chapoton map associated to valued quivers
• Transverse Quiver Grassmannians and Bases in Affine Cluster Algebras