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Keywords:
Weil bundle; Weil algebra; Poisson manifold; Lie derivative; Poisson 2-form
Weil bundle; Weil algebra; Poisson manifold; Lie derivative; Poisson 2-form
Summary:
In this paper, $M$ denotes a smooth manifold of dimension $n$, $A$ a Weil algebra and $M^{A}$ the associated Weil bundle. When $(M,\omega _{M})$ is a Poisson manifold with $2$-form $\omega _{M}$, we construct the $2$-Poisson form $\omega _{M^{A}}^{A}$, prolongation on $M^{A}$ of the $2$-Poisson form $\omega _{M}$. We give a necessary and sufficient condition for that $M^{A}$ be an $A$-Poisson manifold.
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