Database for Fusion Categories

This repository provides a database for fusion categories in different forms.

TensorCategories.jl

This database is accesible via our julia package TensorCategories.jl. Please visit the documentation for detailed information.

AnyonWiki

The multiplicity fusion categories up to rank 7 that are contained are taken from the AnyonWiki. If you use the Data please cite both packages.

julia> using TensorCategories;

julia> C = anyonwiki(3,1,0,2,1,1,1)
Fusion Category 3_1_0_2_1_1_1

julia> print_multiplication_table(C)
3×3 Matrix{String}:
 "𝟙"   "X2"  "X3"
 "X2"  "𝟙"   "X3"
 "X3"  "X3"  "𝟙 ⊕ X2 ⊕ X3"

Centers of multiplicity-free fusion categories up to rank 5

We computed all centers of multiplicty free fusion categories up to rank 5 in https://arxiv.org/abs/2406.13438 and stored them here.

julia> using TensorCategories

julia> Z = anyonwiki_center(3,1,0,2,1,1,1)
Skeletonization of Drinfeld center of Fusion Category 3_1_0_2_1_1_1

julia> print_multiplication_table(Z)
8×8 Matrix{String}:
 "(𝟙, γ)"        "(X2, γ)"       …  "(X2 ⊕ X3, γ)"
 "(X2, γ)"       "(𝟙, γ)"           "(𝟙 ⊕ X3, γ)"
 "(𝟙 ⊕ X2, γ)"   "(𝟙 ⊕ X2, γ)"      "(𝟙 ⊕ X3, γ) ⊕ (X2 ⊕ X3, γ)"
 "(X3, γ1)"      "(X3, γ1)"         "(𝟙 ⊕ X3, γ) ⊕ (X2 ⊕ X3, γ)"
 "(X3, γ2)"      "(X3, γ2)"         "(𝟙 ⊕ X3, γ) ⊕ (X2 ⊕ X3, γ)"
 "(X3, γ3)"      "(X3, γ3)"      …  "(𝟙 ⊕ X3, γ) ⊕ (X2 ⊕ X3, γ)"
 "(𝟙 ⊕ X3, γ)"   "(X2 ⊕ X3, γ)"     "(X2, γ) ⊕ (𝟙 ⊕ X2, γ) ⊕ (X3, γ1) ⊕ (X3, γ2) ⊕ (X3, γ3)"
 "(X2 ⊕ X3, γ)"  "(𝟙 ⊕ X3, γ)"      "(𝟙, γ) ⊕ (𝟙 ⊕ X2, γ) ⊕ (X3, γ1) ⊕ (X3, γ2) ⊕ (X3, γ3)"

If you use this data please cite the article as follows:

@software{Maeurer2026TensorCategories,
  author    = {M{\"a}urer, Fabian},
  title     = {{TensorCategories.jl}},
  year      = {2026},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.18760250},
  url       = {https://doi.org/10.5281/zenodo.18760250}
}

Center of the Haagerup subfactor

We computed the center of the Haagerup fusion category in https://arxiv.org/abs/2601.20012 and stored it here.

julia> using TensorCategories

# this is faster and what most people are probably more interested in
Z = numeric_unitary_center_H3()
Fusion Category with 12 simple objects

# Warning: this takes 30 min
julia> Z = haagerup_H3_center();

License

The TensorCategoriesDatabase is licensed under the GNU General Public License v3.0 or later.

Copyright (c) 2021 Fabian Mäurer and contributors.

See LICENSE for the full license text. See COPYRIGHT for copyright information.