Geodesic
Poisson Geometry Related to Atiyah Sequences
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct and investigate a short exact sequence of Poisson $\mathcal{V}\!\mathcal{B}$-groupoids which is canonically related to the Atiyah sequence of a $G$-principal bundle $P$. Our results include a description of the structure of the symplectic leaves of the Poisson groupoid $\frac{T^*P\times T^*P}{G}\rightrightarrows \frac{T^*P}{G}$. The semidirect product case, which is important for applications in Hamiltonian mechanics, is also discussed.
Keywords: Atiyah sequence; $\mathcal{VB}$-groupoid; Poisson groupoid; dualization of $\mathcal{VB}$-groupoid. 
@article{SIGMA_2018_14_a4,
     author = {Kirill Mackenzie and Anatol Odzijewicz and Aneta Sli\.zewska},
     title = {Poisson {Geometry} {Related} to {Atiyah} {Sequences}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a4/}
}
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Kirill Mackenzie; Anatol Odzijewicz; Aneta Sliżewska. Poisson Geometry Related to Atiyah Sequences. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a4/

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