Integrability and reduction of Hamiltonian actions on Dirac manifolds

Olivier Brahic; Rui Loja Fernandes

doi:10.1016/j.indag.2014.07.007

Integrability and reduction of Hamiltonian actions on Dirac manifolds

Olivier Brahic, Rui Loja Fernandes

Mathematics

Research output: Contribution to journal › Article › peer-review

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:M→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.

Original language	English (US)
Pages (from-to)	901-925
Number of pages	25
Journal	Indagationes Mathematicae
Volume	25
Issue number	5
DOIs	https://doi.org/10.1016/j.indag.2014.07.007
State	Published - Oct 1 2014

Keywords

Dirac structures
Integrability
Moment map
Reduction
Symplectic geometry

ASJC Scopus subject areas

General Mathematics

Online availability

10.1016/j.indag.2014.07.007

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AU - Fernandes, Rui Loja

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AB - 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→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.

KW - Dirac structures

KW - Integrability

KW - Moment map

KW - Reduction

KW - Symplectic geometry

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JF - Indagationes Mathematicae

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ER -

Integrability and reduction of Hamiltonian actions on Dirac manifolds

Abstract

Keywords

ASJC Scopus subject areas

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