Group Cohomology and Gauge Equivalence of some Twisted Quantum Doubles

Details Group Cohomology and Gauge Equivalence of some Twisted Quantum Doubles Group Cohomology and Gauge Equivalence of some Twisted Quantum Doubles

2000-02-29

arxiv.org/abs/math/0002246v1

Trans. Amer. Math. Soc. 353 (2001), 3465-3509

Mathematics

Quantum Algebra

LaTeX, 49 pages

Scientific paper

10.1090/S0002-9947-01-02771-4

Dijkgraaf, Pasquier and Roche introduced twisted quantum doubles of a finite group in the context of conformal field theory. We study equivalences that arise among the braided monoidal categories associated to these quantum doubles, especially in the commutative case. This involves a close study of the cohomology of various complexes introduced by Eilenberg-MacLane. We show among other things that an equivalence of braided monoidal categories is the same as gauge equivalence of the corresponding quantum doubles, and that an invariant for an equivalence class is given by a metabolic quadratic space.

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