The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven

@article{Ooms2011ThePC,
  title={The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven},
  author={A. Ooms},
  journal={Journal of Algebra},
  year={2011},
  volume={365},
  pages={83-113}
}
  • A. Ooms
  • Published 2011
  • Mathematics
  • Journal of Algebra
  • Abstract Let g be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We collect some general results on the Poisson center of S ( g ) , including some simple criteria regarding its polynomiality, and also on certain Poisson commutative subalgebras of S ( g ) . These facts are then used to complete our previous work on the subject (Ooms, 2009 [O5, 5] ), i.e. to give an explicit description for the Poisson center of all indecomposable, nilpotent Lie… CONTINUE READING
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