Levi decomposition for smooth Poisson structures

@article{Monnier2002LeviDF,
  title={Levi decomposition for smooth Poisson structures},
  author={P. Monnier and N. T. Zung},
  journal={Journal of Differential Geometry},
  year={2002},
  volume={68},
  pages={347-395}
}
We prove the existence of a local smooth Levi decomposition for smooth Poisson structures and Lie algebroids near a singular point. This Levi decomposition is a kind of normal form or partial linearization, which was established in the formal case by Wade [Wad97] and in the analytic case by the second author [Zun03]. In particular, in the case of smooth Poisson structures with a compact semisimple linear part, we recover Conn’s smooth linearization theorem [Con85], and in the case of smooth Lie… Expand
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