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The aim of this chapter is to present Drinfeld’s concepts of (braided) quasi-bialgebra and of gauge transformation. These concepts will be needed to express the main results of Part IV. The definitions given here are based on the formalism of tensor categories and tensor functors introduced in Chapters XI and XIII. In Section 4 we construct braid group representa-tions for any braided quasi-bialgebra and we show that equivalent braided quasi-bialgebras give rise to equivalent representations.
KeywordsGauge Transformation Hopf Algebra Braid Group Invertible Element Tensor Category
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