Prolongation of Poisson $2$-form on Weil bundles

Moukala, Norbert Mahoungou ; Bossoto, Basile Guy Richard

Archivum mathematicum, Tome 52 (2016) no. 2, pp. 91-111.

Résumé

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.

Détail

DOI : 10.5817/AM2016-2-91

Classification : 17D63, 53D05, 53D17, 58A20, 58A32
Keywords: Weil bundle; Weil algebra; Poisson manifold; Lie derivative; Poisson 2-form