Computations of Nambu–Poisson Cohomologies: Case of Nambu–Poisson Tensors of Order 3 on ℝ⁴

Abstract

We compute Nambu–Poisson cohomology for Nambu–Poisson tensors of order three which are defined on ℝ4. In particular, we prove that Nambu–Poisson cohomology of exact Nambu–Poisson tensors is equivalent to relative cohomology.