Note on Poisson cohomology on Weil bundles
Volume 122 / 2019
Annales Polonici Mathematici 122 (2019), 1-9
MSC: Primary 53D17; Secondary 58A20.
DOI: 10.4064/ap180207-22-10
Published online: 8 February 2019
Abstract
The purpose of this note on Poisson cohomology is to show that if $M$ is a Poisson manifold and if $A$ is a Weil algebra, then the Weil bundle $M^{A}$ is a Poisson manifold. Therefore, we establish a relationship between Poisson cohomology $H_{\{\cdot ,\cdot \}_{A}}^{\bullet }(M^{A},A)$ with values in $A$ and Poisson cohomology $H_{\{\cdot ,\cdot \},\mathbb {R}}^{\bullet }(M^{A})$ with real values.
