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This Poisson structure arises in the combinatorial description of the phase space of Chern-Simons theory with gauge group $G\\ltimes\\mathfrak{g}^*$ on $R \\times S_{g,n}$, where S_{g,n} is a surface of genus g with n punctures. The quantisation of this Poisson structure is a key step in the quantisation of Chern-Simons theory with gauge group $G\\ltimes\\mathfrak{g}^*$. 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