Cluster algebras arising from the infinity-gon

TL;DR

This paper introduces a new construction of cluster algebras of type A_infinity, classifies those arising from the infinity-gon, and establishes an equivalence with the infinite cluster category of the same type.

Contribution

It provides a complete classification of cluster algebras from the infinity-gon and links their diagonals to the infinite cluster category, expanding understanding of infinite type cluster algebras.

Findings

Complete classification of cluster algebras from the infinity-gon

Construction of the diagonals category and its triangle-equivalence

Connection to the infinite cluster category of type A_infinity

Abstract

We introduce a handy construction of cluster algebras of type $\mathbb{A}_{\infty}$, we give a complete classification of the cluster algebras arising from the infinity-gon, and finally we construct the category of the diagonals of the infinity-gon and show that it is triangle-equivalent to the infinite cluster category of type $\mathbb{A}_{\infty}$ described by Holm and J{\o}rgensen.