Solutions of the hexagon equation for abelian anyons

TL;DR

This paper investigates the conditions under which solutions to the hexagon equation exist for abelian anyons and classifies prime abelian anyons, advancing understanding of their mathematical structure.

Contribution

It provides a classification of prime abelian anyons and analyzes obstructions to solving the hexagon equation in abelian fusion rules.

Findings

Identified obstructions to hexagon equation solutions for abelian anyons

Classified prime abelian anyons based on their fusion properties

Enhanced understanding of the mathematical framework of abelian anyons

Abstract

We address the problem of determining the obstruction to the existence of solutions of the hexagon equation for abelian fusion rules and the classification of prime abelian anyons.