Geodesic
Poisson Principal Bundles
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space $X$ is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson–Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant connection, and the base has an inherited Poisson structure and Poisson-compatible contravariant connection. The latter are known to be the semiclassical data for a quantum differential calculus. The theory is illustrated by the Poisson level of the $q$-Hopf fibration on the standard $q$-sphere. We also construct the Poisson level of the spin connection on a principal bundle.
Keywords: noncommutative geometry, quantum group gauge theory, symplectic geometry, Poisson geometry, Lie bialgebra, homogenous space
Mots-clés : $q$-monopole. 
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     author = {Shahn Majid and Liam Williams},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a5/}
}
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Shahn Majid; Liam Williams. Poisson Principal Bundles. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a5/

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