TensorCategories is a package under development with the intention to provide a framework as well a examples for computations in the realm of categories.
You need to have Julia installed. To use TensorCategories do the following:
julia> import Pkg
julia> Pkg.add("TensorCategories")TensorCategories relies on the algebraic structures from the OSCAR-System. Here a minimal usage Example.
using TensorCategories, Oscar;
F = GF(5)
G = symmetric_group(2)
X = gset(G,[1,2,3])
C = convolution_category(F,X)
simples(C)
grothendieck_ring(C)
TensorCategories provides a vast framework for constructions with finite tensor categories and especially fusion categories.
The current pinnacle feature is the computation of the center of a fusion category in explicit form. The theoretical ground work for this approach is layed in https://arxiv.org/abs/2406.13438
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).