Elsevier

Indagationes Mathematicae

Volume 25, Issue 5, October 2014, Pages 901-925
Indagationes Mathematicae

Integrability and reduction of Hamiltonian actions on Dirac manifolds

https://doi.org/10.1016/j.indag.2014.07.007Get rights and content
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Abstract

For a Hamiltonian, proper and free action of a Lie group G on a Dirac manifold (M,L), with a regular moment map μ:Mg, the manifolds M/G, μ1(0) and μ1(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 μ1(0) and μ1(0)/G may fail to be integrable, and we describe the obstructions to their integrability.

Keywords

Symplectic geometry
Dirac structures
Moment map
Integrability
Reduction

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