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Lin√©arisation de certaines structures de Poisson. (Linearization of certain Poisson structures). (French) Zbl 0728.58011
The author proves that certain Poisson structures which vanish at a point are linearizable at that point. This result is used to determine the nondegenerate real three-dimensional Lie algebras.

MSC:
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
53D17 Poisson manifolds; Poisson groupoids and algebroids
17B63 Poisson algebras
17B05 Structure theory for Lie algebras and superalgebras
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