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Representation Theory of Twisted Group Double

D. Altschuler·A. Coste·J-M. Maillard
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Abstract

This text collects useful results concerning the quasi-Hopf algebra $\D $. We give a review of issues related to its use in conformal theories and physical mathematics. Existence of such algebras based on 3-cocycles with values in $ {R} / {Z} $ which mimic for finite groups Chern-Simons terms of gauge theories, open wide perspectives in the so called "classification program". The modularisation theorem proved for quasi-Hopf algebras by two authors some years ago makes the computation of topological invariants possible. An updated, although partial, bibliography of recent developments is provided.

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D. Altschuler, A. Coste, J-M. Maillard. 2003-10-02. Representation Theory of Twisted Group Double. https://arxiv.org/abs/hep-th/0309257

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