2006/03/31 by Christopher D. Goff, Christopher Goff, Geoffrey Mason +2
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.GR #math.QA
paper · pdf · doi:10.1016/j.jalgebra.2006.10.022
published as Journal of Algebra, 312 (2007), no. 2, 849--875 · 27 pages, LateX, a few of typos in v2 corrected
arxiv created 2006/10/20 · openalex publication_date 2006/11/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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, w2 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.