Poisson Reduction

  • Juan-Pablo Ortega
  • Tudor S. Ratiu
Part of the Progress in Mathematics book series (PM, volume 222)


The preceding chapters presented various procedures that led to the construction of new symplectic manifolds from Poisson or symplectic manifolds acted canonically upon by a Lie group. The present goal is the description of a general method to obtain new Poisson manifolds, or at least Poisson algebras, by reducing symmetric Poisson manifolds. In parallel, we will show the relationship between these reduced spaces and the symplectic reduced spaces that were previously introduced. References related to this topic are Marsden and Ratiu (1986), Vaisman (1996b), and Ortega and Ratiu (1998).


Open Neighborhood Poisson Bracket Symplectic Form Symplectic Manifold Poisson Structure 
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Copyright information

© Juan Pablo Ortega and Tudor S. Ratiu 2004

Authors and Affiliations

  • Juan-Pablo Ortega
    • 1
  • Tudor S. Ratiu
    • 2
  1. 1.CNRS-Laboratoire de Mathématiques de BensançonUniversité de Franche-Comté, UFR des Sciences et TechniquesBensançon CedexFrance
  2. 2.Départment de MathématiquesLausanneSwitzerland

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