Abstract
For a given quasi-triangular Hopf algebra \(\mathcal{H}\), we study relations between the braided group \(\tilde {\mathcal{H}}^* \) and Drinfeld's twist. We show that the braided bialgebra structure of \(\tilde {\mathcal{H}}^* \) is naturally described by means of twisted tensor powers of \(\mathcal{H}\) and their module algebras. We introduce a universal solution to the reflection equation (RE) and deduce a fusion prescription for RE-matrices.
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