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Definition $:$ Let $H$ be a Hopf algebra. An invertible element $R \in H \otimes H$ is called a coboundary structure on $H$ if $(1)$ $\Delta^{\text {op}} = R \Delta R^{-1},$ $(2)$ $R_{21} = R^{-1},$ $(...

The theorem I am referring to here says that if we start with a Lie bialgebra $\mathfrak g$ determined by some skew-symmetric element $r \in \mathfrak g \otimes \mathfrak g$ satisfying classical Yang-...