Geodesic
The Fock–Rosly Poisson Structure as Defined by a Quasi-Triangular $r$-Matrix
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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We reformulate the Poisson structure discovered by Fock and Rosly on moduli spaces of flat connections over marked surfaces in the framework of Poisson structures defined by Lie algebra actions and quasitriangular $r$-matrices, and we show that it is an example of a mixed product Poisson structure associated to pairs of Poisson actions, which were studied by J.-H. Lu and the author. The Fock–Rosly Poisson structure corresponds to the quasi-Poisson structure studied by Massuyeau, Turaev, Li-Bland, and Ševera under an equivalence of categories between Poisson and quasi-Poisson spaces.
Mots-clés : flat connections; Poisson Lie groups; $r$-matrices; quasi-Poisson spaces. 
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     title = {The {Fock{\textendash}Rosly} {Poisson} {Structure} as {Defined} by a {Quasi-Triangular} $r${-Matrix}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a62/}
}
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Victor Mouquin. The Fock–Rosly Poisson Structure as Defined by a Quasi-Triangular $r$-Matrix. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a62/

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