Modular categories are not determined by their modular data
Quantum Algebra
2021-06-09 v2 Category Theory
Rings and Algebras
Representation Theory
Abstract
Arbitrarily many pairwise inequivalent modular categories can share the same modular data. We exhibit a family of examples that are module categories over twisted Drinfeld doubles of finite groups, and thus in particular integral modular categories.
Cite
@article{arxiv.1708.02796,
title = {Modular categories are not determined by their modular data},
author = {Michaël Mignard and Peter Schauenburg},
journal= {arXiv preprint arXiv:1708.02796},
year = {2021}
}