TensorCategories.jl

TensorCategories.jl is a software package based on the programming language Julia and the open-source computer algebra system Oscar.jl for computations with tensor categories.

Installation

You need to have Julia installed. For reliable results Julia version at least 1.6 is required. To use TensorCategories do the following:

julia> import Pkg
julia> Pkg.add(url = "https://github.com/FabianMaeurer/TensorCategories.jl")

Usage

To use TensorCategories the structures from the OSCAR-System are required. Here a minimal usage example.

julia> using TensorCategories;
julia> I = Ising()Ising fusion category
julia> C = center(Ising())Drinfeld center of Ising fusion category
julia> S = smatrix(C)[   1       1    2    2    4*√2]
[   1       1    2    2   -4*√2]
[   2       2    0   -4       0]
[   2       2   -4    4       0]
[4*√2   -4*√2    0    0       0]

Acknowledgements

This project was started under supervision of Prof. Ulrich Thiel (University of Kaiserslautern). This work is a contribution to the SFB-TRR 195 'Symbolic Tools in Mathematics and their Application' of the German Research Foundation (DFG).