Computations of Nambu-Poisson cohomologies

Abstract

We want to associate to an n-vector on a manifold of dimension n a cohomology which generalizes the Poisson cohomology of a 2-dimensional Poisson manifold. Two possibilities are given here. One of them, the Nambu-Poisson cohomology, seems to be the most pertinent. We study these two cohomologies locally, in the case of germs of n-vectors on 𝕜n(𝕜=ℝ or ℂ).