Poisson Geometry Related to Atiyah Sequences

Abstract

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 $\frac{T^{\ast }P\times T^{\ast }P}{G}\rightrightarrows \frac{T^{\ast }P}{G}$. The semidirect product case, which is important for applications in Hamiltonian mechanics, is also discussed.

Cited by in corpus (2)

• Fibre-wise linear Poisson structures related to W*-algebras
• Atiyah sequence and Gauge transformations of a principal $2$-bundle over a Lie groupoid