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

View/Open
Document typeExternal research report
Defense date2015-03
Rights accessOpen Access
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
CitationMiranda, E. "A note on symplectic and Poisson linearization of semisimple Lie algebra actions". 2015.
URL other repositoryhttp://arxiv.org/pdf/1503.03840v1.pdf
Files | Description | Size | Format | View |
---|---|---|---|---|
1503.03840v1.pdf | 174,8Kb | View/Open |
Except where otherwise noted, content on this work
is licensed under a Creative Commons license
:
Attribution-NonCommercial-NoDerivs 3.0 Spain