Integrability and reduction of Hamiltonian actions on Dirac manifolds

Olivier Brahic, Rui Loja Fernandes

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)901-925
Number of pages25
JournalIndagationes Mathematicae
Volume25
Issue number5
DOIs
StatePublished - Oct 1 2014

Keywords

  • Dirac structures
  • Integrability
  • Moment map
  • Reduction
  • Symplectic geometry

ASJC Scopus subject areas

  • Mathematics(all)

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