On the Gauge Equivalence of Twisted Quantum Doubles of Elementary Abelian and Extra-Special 2-Groups

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dc.creatorGoff, Christopher
dc.creatorMason, Geoffrey
dc.creatorNg, Siu-Hung
dc.date2006-03-08
dc.date2006-10-20
dc.date.accessioned2026-07-07T08:07:39Z
dc.date.available2026-07-07T08:07:39Z
dc.descriptionWe 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.
dc.description27 pages, LateX, a few of typos in v2 corrected
dc.identifierhttps://arxiv.org/abs/math/0603191
dc.identifierhttp://arxiv.org/abs/math/0603191
dc.identifierJournal of Algebra, 312 (2007), no. 2, 849--875
dc.identifierdoi:10.1016/j.jalgebra.2006.10.022
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131003
dc.subjectQuantum Algebra
dc.subjectGroup Theory
dc.titleOn the Gauge Equivalence of Twisted Quantum Doubles of Elementary Abelian and Extra-Special 2-Groups
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