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Nondegeneracy of the Lie algebra aff(n)

Jean-Paul Dufour·Nguyen Tien Zung
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Abstract

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

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Jean-Paul Dufour, Nguyen Tien Zung. 2002-12-24. Nondegeneracy of the Lie algebra aff(n). https://arxiv.org/abs/math/0208036

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