Algorithmic Aspects of Fusion Categories
by
H4
Geomatikum
A model example of a fusion category is the category of all finite-dimensional complex
representations of a finite group: we can add and tensor them, we can take duals, and due to
semisimplicity we have "fusion rules". These features motivate the general notion of fusion
categories, which can be viewed as categorical analogues of finite groups.
The categorical center of a fusion category is again a fusion category, equipped with an
additional structure called braiding---a categorical commutativity property. Braided fusion
categories play an important role in areas such as rational conformal field theories.
Given an explicit fusion category, how can we compute its center in practice? To explore
fusion categories computationally, my PhD student Fabian Mäurer and I developed the software
package TensorCategories.jl, in which we implemented a new general algorithm we devised for
computing centers of fusion categories. Using it, we computed the centers of all 279
multiplicity-free fusion categories up to rank 5. More recently, in collaboration with Gert
Vercleyen, we also computed the center of the Haagerup subfactor H3.
My talk is rather hands-on and includes some live software demonstrations (assuming the
computer cooperates).
Prof. Latschev