List of Small Multiplicity-Free Fusion Categories

Download all numeric solutions of the pentagon and hexagon equations for all multiplicity free fusion categories up to and including rank 7 here.

The numeric solutions are organized as follows. For each fusion ring there is a folder corresponding to one of its categories where files can be found for the pentagon, hexagon, and pivotal structures. There is also a file that lists all indices of the nonzero structure constants. The pentsol files contain rows of tab-separated numbers of which the first 6 correspond to the object labels and the last two to the real and imaginary parts of the corresponding F-symbol. A similar convention is used for the solutions to the hexagon and pivotal equations. All rings and categories in these files should be labeled the same way as on this web site.

The symbolic solutions are available as part of the Anyonica and the TensorCategories.jl packages. Any category with formal name can be obtained be evaluating the following code

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