Mutation invariants of cluster algebras of rank 2

2024/01/18 by Zhichao Chen, Chen, Zhichao, Zixu Li +1 · 1 citation
Mathematics · #11D09 #11D25 #13F60 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2401.09704

openalex publication_date 2024/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the mutation invariants of cluster algebras of rank 2. We characterize the mutation invariants of finite type. Two examples are provided for the affine type and we prove the non-existence of Laurent mutation invariants of non-affine type. As an application, a class of Diophantine equations encoded with cluster algebras are studied.

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