Nondegeneracy of the Lie algebra aff(n)

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.

Some typos corrected. To appear in CRAS Paris