Nondegeneracy of the Lie algebra $ \mathfrak{aff}\mathrm{(n)}$

Jean-Paul Dufour; Nguyen Tien Zung

doi:10.1016/S1631-073X(02)02599-2

Nondegeneracy of the Lie algebra

𝔞𝔣𝔣 (n)

Jean-Paul Dufour ¹; Nguyen Tien Zung ²

¹ GTA, UMR 5030 CNRS, Département de mathématiques, Université Montpellier II, 34095 Montpellier cedex 5, France
² Laboratoire Emile Picard, UMR 5580 CNRS, UFR MIG, Université Toulouse III, 31062 Toulouse cedex 4, France

Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 1043-1046.

Abstract
Résumé

We show that $𝔞𝔣𝔣 (n)$ , the Lie algebra of affine transformations of $ℝ^{n},$ 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 $𝔞𝔣𝔣 (n)$ is locally analytically (resp., formally) linearizable.

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 $𝔞𝔣𝔣 (n)$ des transformations affines sur $ℝ^{n}$ , est localement analytiquement (resp., formellement) linéarisable.

Received: 2002-09-24
Accepted: 2002-10-15
Published online: 2002-11-16

DOI: 10.1016/S1631-073X(02)02599-2

Author's affiliations:

Jean-Paul Dufour ¹; Nguyen Tien Zung ²

¹ GTA, UMR 5030 CNRS, Département de mathématiques, Université Montpellier II, 34095 Montpellier cedex 5, France
² Laboratoire Emile Picard, UMR 5580 CNRS, UFR MIG, Université Toulouse III, 31062 Toulouse cedex 4, France

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     author = {Jean-Paul Dufour and Nguyen Tien Zung},
     title = {Nondegeneracy of the {Lie} algebra $ \mathfrak{aff}\mathrm{(n)}$},
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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/

References
Cited by

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