Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Entire DC Network
On The Gauge Equivalence Of Twisted Quantum Doubles Of Elementary Abelian And Extra-Special 2-Groups, Christopher Goff, Geoffrey Mason, Siu-Hung Ng
On The Gauge Equivalence Of Twisted Quantum Doubles Of Elementary Abelian And Extra-Special 2-Groups, Christopher Goff, Geoffrey Mason, Siu-Hung Ng
Christopher Goff
We establish braided tensor equivalences among module categories over the twisted quantum double of a finite group defined by an extension of a group H by an abelian group, with 3-cocycle inflated from a 3-cocycle on H. We also prove that the canonical ribbon structure of the module category of any twisted quantum double of a finite group is preserved by braided tensor equivalences. We give two main applications: first, if G is an extra-special 2-group of width at least 2, we show that the quantum double of G twisted by a 3-cocycle w is gauge equivalent to a twisted …