Integral bases of cluster algebras and representations of tame quivers

2009/01/14 by Ming Ding, Jie Xiao, Ding, Ming +3 · 1 citation
Mathematics · Physics and Astronomy · #14M99 #16G20 #16G99 #17B35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0901.1937

openalex publication_date 2009/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In \citeCK2005 and \citeSZ, the authors constructed the bases of cluster algebras of finite types and of type \widetildeA_1,1, respectively. In this paper, we will deduce ℤ-bases for cluster algebras of affine types.

Citations

• Cluster algebra structures and semicanonical bases for unipotent groups
• On the cluster multiplication theorem for acyclic cluster algebras

Cited by

• Positivity for Regular Cluster Characters in Acyclic Cluster Algebras

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• Cluster algebras as Hall algebras of quiver representations
• Generic bases for cluster algebras from the cluster category
• Transverse Quiver Grassmannians and Bases in Affine Cluster Algebras
• Generic Variables in Acyclic Cluster Algebras and Bases in Affine Cluster Algebras