Poisson Geometry Related to Atiyah Sequences
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∗PG⇉T∗PG. The semidirect product case, w...
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| Sprache: | eng |
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| Zusammenfassung: | 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∗PG⇉T∗PG. The semidirect product case, which is important for applications in Hamiltonian mechanics, is also discussed. |
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| DOI: | 10.3842/SIGMA.2018.005 |