On a Poisson foliation equipped with a canonical and cotangential action of a compact Lie group, we describe the averaging method for Poisson connections. In this context, we generalize some previous results on Hannay-Berry connections for Hamiltonian and locally Hamiltonian actions on Poisson fiber bundles. Our main application of the averaging method for connections is the construction of invariant Dirac structures parametrized by the 2-cocycles of the de Rham-Casimir complex of the Poisson foliation.
Bibliographical noteFunding Information:
70G45. Key words and phrases. Poisson foliation, cotangential group action, invariant Ehresmann connections, averaging method, pre-momentum map, Dirac structure . The authors are supported by CONACYT grant CB2015 no. 258302. E. Velasco - Barreras was supported by FAPERJ grants E-26/202.411/2019 and E-26/202.412/2019. ∗ Corresponding author: Misael Avendaño-Camacho.
© American Institute of Mathematical Sciences.
- Averaging method
- Cotangential group action
- Dirac structure
- Invariant ehresmann connections
- Poisson foliation
- Pre-momentum map