International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 2, Pages 65-81

Computations of Nambu-Poisson cohomologies

Philippe Monnier

Département de Mathématiques, Université Montpellier II, Place Eugène Bataillon 34095, Montpellier Cedex 5, France

Received 29 September 2000

Copyright © 2001 Philippe Monnier. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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=or).