Integrability and Reduction of Hamiltonian Actions on Dirac Manifolds

For a Hamiltonian, proper and free action of a Lie group $G$ on a Dirac manifold $(M,L)$, with a regular moment map $μ:M\to \mathfrak{g}^*$, the manifolds $M/G$, $μ^{-1}(0)$ and $μ^{-1}(0)/G$ all have natural induced Dirac structures. If $(M,L)$ is an integrable Dirac structure, we show that $M/G$ is always integrable, but $μ^{-1}(0)$ and $μ^{-1}(0)/G$ may fail to be integrable, and we describe the obstructions to their integrability.

No reviews yet.

No comments yet.