Laurent phenomenon algebras arising from surfaces

TL;DR

This paper establishes a connection between Laurent phenomenon algebras and cluster algebras arising from both orientable and non-orientable surfaces, broadening the scope of algebraic structures linked to geometric surfaces.

Contribution

It extends the framework of Laurent phenomenon algebras to include unpunctured surfaces of both orientable and non-orientable types.

Findings

Both orientable and non-orientable unpunctured surfaces have associated LP-algebras.

The work links cluster algebras from surfaces to Laurent phenomenon algebras.

It generalizes previous constructions to a wider class of surfaces.

Abstract

It was shown by Fomin, Shapiro and Thurston that some cluster algebras arise from orientable surfaces. Subsequently, Dupont and Palesi extended this construction to non-orientable surfaces. We link this framework to Lam and Pylyavskyy's Laurent phenomenon algebras, showing that both orientable and non-orientable unpunctured marked surfaces have an associated LP-algebra.