Poisson brackets of even symplectic forms on the algebra of differential forms

TL;DR

This paper introduces a non-degenerate even Poisson bracket on the algebra of differential forms derived from a symplectic form and a pseudo-Riemannian metric, comparing it with the Koszul-Schouten bracket.

Contribution

It defines a new Poisson bracket structure on differential forms and analyzes its properties, contrasting it with existing brackets like Koszul-Schouten.

Findings

The new Poisson bracket is non-degenerate and even.

It exhibits specific algebraic properties distinct from the Koszul-Schouten bracket.

The paper establishes a detailed comparison between the two brackets.

Abstract

Given a symplectic form and a pseudo-riemannian metric on a manifold, a non degenerate even Poisson bracket on the algebra of differential forms is defined and its properties are studied. A comparison with the Koszul-Schouten bracket is established.