Mathematics – Quantum Algebra
Scientific paper
2006-03-08
Journal of Algebra, 312 (2007), no. 2, 849--875
Mathematics
Quantum Algebra
27 pages, LateX, a few of typos in v2 corrected
Scientific paper
10.1016/j.jalgebra.2006.10.022
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 quantum double of an elementary abelian 2-group if, and only if, w^2 is trivial; second, we discuss the gauge equivalence classes of twisted quantum doubles of groups of order 8, and classify the braided tensor equivalence classes of these quasi-triangular quasi-bialgebras. It turns out that there are exactly 20 such equivalence classes.
Goff Christopher
Mason Geoffrey
Ng Siu-Hung
No associations
LandOfFree
On the Gauge Equivalence of Twisted Quantum Doubles of Elementary Abelian and Extra-Special 2-Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the Gauge Equivalence of Twisted Quantum Doubles of Elementary Abelian and Extra-Special 2-Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Gauge Equivalence of Twisted Quantum Doubles of Elementary Abelian and Extra-Special 2-Groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-447149