On Low-Rank Multiplicity-Free Complex Fusion Categories

Source abstract

Abstract This paper explains the methods and algorithms we used to obtain explicit F -symbols, R -symbols, and pivotal coefficients of what we believe are all multiplicity-free pivotal complex fusion categories up to rank 7. Particular attention is given to how the individual steps for solving the consistency equations are done with Anyonica, a software package we developed for working with fusion categories. Gauge and automorphism equivalence are reviewed and a method to remove equivalent categories via a gauge-split basis is given. A census of all multiplicity-free fusion categories up to rank 7, along with all compatible braided and pivotal structures, is presented, and comments on their general properties are given.