Quantum Teichmuller theory and representations of the pure braid group

TL;DR

This paper applies quantum Teichmüller theory techniques to develop a new family of representations for the pure braid group on a sphere, advancing understanding of its algebraic structure.

Contribution

It introduces a novel approach by adapting quantum Teichmüller methods to construct representations of the pure braid group on the sphere.

Findings

Constructed a new family of pure braid group representations.

Extended quantum Teichmüller theory to spherical cases.

Provides tools for further algebraic and geometric analysis.

Abstract

We adapt some of the methods of quantum Teichm\"uller theory to construct a family of representations of the pure braid group of the sphere.