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Letters in Mathematical Physics

, Volume 65, Issue 3, pp 213–227 | Cite as

Linearity of the Transverse Poisson Structure to a Coadjoint Orbit

  • Inês Cruz
  • Tiago Fardilha
Article

Abstract

We prove a simple formula for the transverse Poisson structure to a coadjoint orbit (in the dual of a Lie algebra \(\mathfrak{g}\)) and use it in examples such as \(\mathfrak{s}\mathfrak{o}\left( 4 \right)*\) and \(\mathfrak{s}\mathfrak{p}\left( 4 \right)*\). We also give a sufficient condition on the isotropy subalgebra of \(\mu \in \mathfrak{g}^*\) so that the transverse Poisson structureto the coadjoint orbit of μ is linear.

coadjoint orbits Lie algebras Poisson manifolds 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Inês Cruz
    • 1
  • Tiago Fardilha
    • 2
  1. 1.Departamento de Matemática AplicadaCentro de Matemática da Universidade do PortoPortoPortugal
  2. 2.Escola Superior de Tecnologia e GestãoInstituto Politécnico de BragançaBragançaPortugal

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