Useful software for working with fusion rings, fusion categories, and anyon models.
- Kac: Kac is an acronym that stands for “Komputations with Algebras and Currents”. The main purpose of “Kac” is to compute fusion rules for Rational Conformal Field Theories based on affine Lie Algebras and their simple current extensions. This includes most coset CFT’s and their tensor products.
- Alatc: Mathematica package for calculating the F- and R- symbols from the quantum groups associated with (non-twisted) affine Lie algebras, as well as the associated modular data, both numerically and in exact form.
- Anyonica.wl: Mathematica package designed to explore and calculate properties of fusion rings and categories. It contains an extensive list of fusion rings, fusion categories, and many functions for working with these structures.
- tensorcategories.jl: a package under development with the intention to provide a framework as well a examples for computations in the realm of categories.
- Jacob Bridgeman’s Repository: a GitHub repository with data for all multiplicity free unitary fusion categories of rank ≤ 6 up to equivalence. For those with braidings, all inequivalent braidings are included.
- tensorkit.jl: A Julia package for large-scale tensor computations, with a hint of category theory. This package can be extended by categorydata.jl to compute with fusion categories.
- W. Aboumrad, has included functions to work with fusion categories in SAGE. See for example the functions to find The F-Matrix of a Fusion Ring
- FusionCategories: T. Hagge and M. Titsworth created a Mathematica package for playing with the arithmetic data associated to fusion categories. This package contains data for a variety of fusion categories including the rank 8 categories Grothendieck equivalent to the representation category of the quantum double of S3 and Grothendieck equivalent rank 11 categories of Frobenius-Perron dimension 32. It contains data for rigidity, pivotal, and braiding structures and does things like calculate S and T matrices. Given the arithmetic data for two multiplicity free, Grothendieck equivalent fusion categories, it also includes a fast algorithm for determining whether or not they are monoidally equivalent.
- Z. Liu, S. Palcoux, and Y. Ren have implemented various categorifiability criteria in SageMath.
- S. Palcoux also has several implementations of SageMath code to find fusion rings with certain properties.