Automorphisms of cluster algebras of rank 2

TL;DR

This paper determines the automorphism group of affine surfaces whose coordinate rings are rank 2 cluster algebras, providing insights into their symmetries and structure.

Contribution

It explicitly computes the automorphism group for rank 2 cluster algebra related affine surfaces, a novel classification in this context.

Findings

Automorphism group characterized for rank 2 cluster algebra surfaces

Identification of symmetries specific to these algebraic structures

Enhanced understanding of the automorphism structure in low-rank cluster algebras

Abstract

We compute the automorphism group of the affine surfaces with the coordinate ring isomorphic to a cluster algebra of rank 2.