Note on Poisson cohomology on Weil bundles

TL;DR

This paper establishes an isomorphism between Poisson cohomology with values in Weil algebras and tensor products of real-valued Poisson cohomology, enhancing understanding of Poisson structures on Weil bundles.

Contribution

It proves that Poisson cohomology with coefficients in a Weil algebra is isomorphic to the tensor product of that algebra with real-valued Poisson cohomology, providing a new structural insight.

Findings

Poisson cohomology with Weil algebra coefficients is isomorphic to tensor product with real cohomology.

The isomorphism simplifies the study of Poisson cohomology on Weil bundles.

The result generalizes previous understanding of Poisson cohomology structures.

Abstract

Let M be a Poisson manifold and A a Weil algebra. We describe an isomorphism of cohomolgy algebra and proves that Poisson cohomology with values in A is isomorphic to the tensor product of A with Poisson cohomolgy with real values.