TY - JOUR

T1 - Computing modular data for pointed fusion categories

AU - Gruen, Angus

AU - Morrison, Scott

N1 - Publisher Copyright:
Indiana University Mathematics Journal ©,

PY - 2021

Y1 - 2021

N2 - A formula for the modular data of Z(VecωG) was given by Coste, Gannon, and Ruelle in [9], but without an explicit proof for arbitrary 3-cocycles. This paper presents a derivation using the representation category of the quasi Hopf algebra DωG. Further, we have written code to compute this modular data for many pairs of small finite groups and 3-cocycles. This code is optimised by taking advantage of 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.

AB - A formula for the modular data of Z(VecωG) was given by Coste, Gannon, and Ruelle in [9], but without an explicit proof for arbitrary 3-cocycles. This paper presents a derivation using the representation category of the quasi Hopf algebra DωG. Further, we have written code to compute this modular data for many pairs of small finite groups and 3-cocycles. This code is optimised by taking advantage of 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.

UR - http://www.scopus.com/inward/record.url?scp=85106289724&partnerID=8YFLogxK

U2 - 10.1512/IUMJ.2021.70.8309

DO - 10.1512/IUMJ.2021.70.8309

M3 - Article

SN - 0022-2518

VL - 70

SP - 561

EP - 593

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 2

ER -