Positivity for quantum cluster algebras from unpunctured orbifolds

TL;DR

This paper derives a quantum Laurent expansion formula for quantum cluster algebras from unpunctured orbifolds with arbitrary coefficients and quantization, establishing positivity for this class of algebras.

Contribution

It provides the first explicit quantum Laurent expansion formula for these orbifold-based quantum cluster algebras, confirming their positivity.

Findings

Quantum Laurent expansion formula derived

Positivity of these quantum cluster algebras established

Applicable to orbifolds with weights of orbifold points equal to 2

Abstract

We give the quantum Laurent expansion formula for the quantum cluster algebras from unpunctured orbifolds with arbitrary coefficients and quantization. As an application, positivity for such class of quantum cluster algebras is given. For technical reasons, it will always be assumed that the weights of the orbifold points are 2.