Fusion categories from the AnyonWiki
In [5] they were able to compute all multiplicity free fusion catogories up to rank 7. In cooperation with the author we were able to include the full database into the package.
The naming
Please visit their website AnyonWiki for the details on the naming scheme. The categories are given by 7 indices
\[(i,j,k,l,m,n,o)\]
where
- $i$ is the rank, i.e the number of simple objects
- $j$ is the multiplicity
- $k$ is the number of not self-dual simples
- $l$ is the index of the fusion rules
- $m$ is the index of the associator
- $n$ is the index of the braiding - 0 if not braided
- $o$ is the index of the pivotal structure
Access
The categories of the AnyonWiki can be accessed as instances of SixJCategory via the function
TensorCategories.anyonwiki — Functionanyonwiki(r,m,n,i,a,b,p)Load the fusion category from the list of multiplicity free fusion categories of rank ≤ 7 with index (r,m,n,i,a,b,p).