On the generalizations of Poisson structures

TL;DR

This paper explores the extension and generalization of Poisson structures, focusing on Nambu-Poisson tensors, their homology and cohomology, and their physical implications.

Contribution

It extends the characterization of Nambu-Poisson tensors within generalized Poisson structures to odd orders and compares their homological properties.

Findings

Nambu-Poisson tensors are characterized as a subfamily of generalized Poisson structures.

Comparison of homology and cohomology complexes for both structures.

Discussion of physical implications of these generalized structures.

Abstract

The characterization of the Nambu-Poisson n-tensors as a subfamily of the Generalized-Poisson ones recently introduced (and here extended to the odd order case) is discussed. The homology and cohomology complexes of both structures are compared, and some physical considerations are made.