English

Computing Modular Data for Pointed Fusion Categories

Quantum Algebra 2019-09-30 v3 Category Theory

Abstract

A formula for the modular data of Z(VecωG)\mathcal{Z}(Vec^{\omega}G) was given by Coste, Gannon and Ruelle in arXiv:hep-th/0001158, but without an explicit proof for arbitrary 3-cocycles. This paper presents a derivation using the representation category of the quasi Hopf algebra DωGD^{\omega}G. Further, we have written code to compute this modular data for many pairs of small finite groups and 3-cocycles. This code is optimised using Galois symmetries of the S and T matrices. We have posted a database of modular data for the Drinfeld center of every Morita equivalence class of pointed fusion categories of dimension less than 64.

Keywords

Cite

@article{arxiv.1808.05060,
  title  = {Computing Modular Data for Pointed Fusion Categories},
  author = {Angus Gruen and Scott Morrison},
  journal= {arXiv preprint arXiv:1808.05060},
  year   = {2019}
}

Comments

28 pages, 4 figures, 7 pages of appendices. v2 update fixes the arXiv reference in the abstract. v3 update: due to recent work the size of the database was increased adding in the modular data for groups with order 48-63 inclusive. Additionally parts of the paper have been re-written based off referee suggestions