Geodesic
Lie Groups in Quasi-Poisson Geometry and Braided Hopf Algebras
Documenta mathematica, Tome 22 (2017), pp. 953-972.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We extend the notion of Poisson-Lie groups and Lie bialgebras from Poisson to $\frak{g}$-quasi-Poisson geometry and provide a quantization to braided Hopf algebras in the corresponding Drinfeld category. The basic examples of these $\frak{g}$-quasi-Poisson Lie groups are nilpotent radicals of parabolic subgroups. We also provide examples of moment maps in this new context coming from moduli spaces of flat connections on surfaces.
Classification : 53D17, 16T05, 53D55, 16T10
Keywords: Poisson-Lie groups, Lie bialgebras, moment map, deformation quantization, $\mathfrak{g}$-quasi-Poisson groups 
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     author = {\v{S}evera, Pavol and Valach, Fridrich},
     title = {Lie {Groups} in {Quasi-Poisson} {Geometry} and {Braided} {Hopf} {Algebras}},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a26/}
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Ševera, Pavol; Valach, Fridrich. Lie Groups in Quasi-Poisson Geometry and Braided Hopf Algebras. Documenta mathematica, Tome 22 (2017), pp. 953-972. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a26/