Nondegeneracy of the Lie algebra aff(n)

الأصل · EN

We show that aff(n), the Lie algebra of affine transformations of Rⁿ, 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.