Bases for cluster algebras from surfaces

TL;DR

This paper constructs two explicit bases for cluster algebras derived from triangulated surfaces without punctures, expanding understanding of their algebraic structure.

Contribution

It introduces two new bases for surface-based cluster algebras within the context of principal coefficients, a novel contribution to the field.

Findings

Constructed two bases for each surface cluster algebra

Applicable to algebras with principal coefficients

Enhances understanding of algebraic structure from surfaces

Abstract

We construct two bases for each cluster algebra coming from a triangulated surface without punctures. We work in the context of a coefficient system coming from a full-rank exchange matrix, for example, principal coefficients.