[Non-dégénérescence de l'algèbre de Lie ]
Nous montrons que toute structure de Poisson analytique (resp., formelle), qui s'annule en un point et dont la partie linéaire correspond à l'algèbre des transformations affines sur , est localement analytiquement (resp., formellement) linéarisable.
We show that , the Lie algebra of affine transformations of is formally and analytically nondegenerate in the sense of A. Weinstein. This means that every analytic (resp., formal) Poisson structure vanishing at a point with a linear part corresponding to is locally analytically (resp., formally) linearizable.
Accepté le :
Publié le :
Jean-Paul Dufour 1 ; Nguyen Tien Zung 2
@article{CRMATH_2002__335_12_1043_0, author = {Jean-Paul Dufour and Nguyen Tien Zung}, title = {Nondegeneracy of the {Lie} algebra $ \mathfrak{aff}\mathrm{(n)}$}, journal = {Comptes Rendus. Math\'ematique}, pages = {1043--1046}, publisher = {Elsevier}, volume = {335}, number = {12}, year = {2002}, doi = {10.1016/S1631-073X(02)02599-2}, language = {en}, }
Jean-Paul Dufour; Nguyen Tien Zung. Nondegeneracy of the Lie algebra $ \mathfrak{aff}\mathrm{(n)}$. Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 1043-1046. doi : 10.1016/S1631-073X(02)02599-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02599-2/
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