Higher Degree Poisson Structures

  • Camille Laurent-Gengoux
  • Anne Pichereau
  • Pol Vanhaecke
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 347)

Abstract

In this chapter we consider weight homogeneous Poisson structures, the simplest of which (homogeneous Poisson structures of degree 0 or 1) have been considered in the previous chapters. Other distinguished classes of weight homogeneous Poisson structures, considered in this chapter, are quadratic Poisson structures (for which a partial classification is given, with the help of the modular vector field), rank two Poisson structures arizing from weight homogeneous Nambu–Poisson structures and the transverse Poisson structures to adjoint orbits in a semi-simple Lie algebra.

Keywords

Poisson Structure Vector Space Versus Nilpotent Orbit Fundamental Identity Casimir Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Camille Laurent-Gengoux
    • 1
  • Anne Pichereau
    • 2
  • Pol Vanhaecke
    • 3
  1. 1.CNRS UMR 7122, Laboratoire de MathématiquesUniversité de LorraineMetzFrance
  2. 2.CNRS UMR 5208, Institut Camille JordanUniversité Jean MonnetSaint-EtienneFrance
  3. 3.CNRS UMR 7348, Lab. Mathématiques et ApplicationsUniversité de PoitiersFuturoscope ChasseneuilFrance

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