Poisson Geometry Related to Atiyah Sequences - Mackenzie, K.; Odzijewicz, A.; Sliżewska, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2018)
We construct and investigate a short exact sequence of Poisson VB-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 T*P×T*P/G⇉T*P/G. The semidirect product case, which is important for applications in Hamiltonian mechanics, is also discussed.