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arXiv · 1503.03840

A note on symplectic and Poisson linearization of semisimple Lie algebra actions

Eva Miranda
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Abstract

In this note we prove that an analytic symplectic action of a semisimple Lie algebra can be locally linearized in Darboux coordinates. This result yields simultaneous analytic linearization for Hamiltonian vector fields in a neighbourhood of a common zero. We also provide an example of smooth non-linearizable Hamiltonian action with semisimple linear part. The smooth analogue only holds if the semisimple Lie algebra is of compact type. An analytic equivariant b-Darboux theorem for b-Poisson manifolds and an analytic equivariant Weinstein splitting theorem for general Poisson manifolds are also obtained in the Poisson setting.

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Eva Miranda. 2015-03-12. A note on symplectic and Poisson linearization of semisimple Lie algebra actions. https://arxiv.org/abs/1503.03840

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