Geodesic
Lie Groups in Quasi-Poisson Geometry and Braided Hopf Algebras
Documenta mathematica, Tome 22 (2017), pp. 953-972
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We extend the notion of Poisson-Lie groups and Lie bialgebras from Poisson to g-quasi-Poisson geometry and provide a quantization to braided Hopf algebras in the corresponding Drinfeld category. The basic examples of these 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.
DOI : 10.4171/dm/583
Classification : 16T05, 16T10, 53D17, 53D55
Mots-clés : deformation quantization, moment map, Poisson-Lie groups, Lie bialgebras, g-quasi-Poisson groups 
@article{10_4171_dm_583,
     author = {Fridrich Valach and Pavol \v{S}evera},
     title = {Lie {Groups} in {Quasi-Poisson} {Geometry} and {Braided} {Hopf} {Algebras}},
     journal = {Documenta mathematica},
     pages = {953--972},
     year = {2017},
     volume = {22},
     doi = {10.4171/dm/583},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/583/}
}
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Fridrich Valach; Pavol Ševera. Lie Groups in Quasi-Poisson Geometry and Braided Hopf Algebras. Documenta mathematica, Tome 22 (2017), pp. 953-972. doi: 10.4171/dm/583

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