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Linearity of the Transverse Poisson Structure to a Coadjoint Orbit

Authors:	Cruz Inês Fardilha Tiago

Institution:	(1) Departamento de Matemática Aplicada, Centro de Matemática da Universidade do Porto, Ruado Campo Alegre 687, 4169-007 Porto, Portugal;(2) Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Bragança, Campus de Santa Apolónia, 5301-854 Bragança, Portugal

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 is linear.

Keywords:	coadjoint orbits Lie algebras Poisson manifolds
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