Computations of Nambu-Poisson cohomologies

Computations of Nambu-Poisson cohomologies

In this paper, we want to associate to a 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).

Dynamics of generalized Poisson and Nambu–Poisson brackets

A Survey on Nambu–Poisson Brackets

The paper provides a survey of known results on geometric aspects related to Nambu-Poisson brackets.

Nambu–Poisson reformulation of the finite dimensional dynamical systems

In this paper we introduce a system of nonlinear ordinary differential equations which in a particular case reduces to Volterra’s system. We found in two simplest cases the complete sets of the integrals of motion using Nambu–Poisson reformulation of the Hamiltonian dynamics. In these cases we have solved the systems by quadratures.

Non-antisymmetric versions of Nambu-Poisson and Lie algebroid brackets

We show that we can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi identity must be skew-symmetric. A similar result holds for a non-antisymmetric version of Lie algebroids.