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 -