Poisson structures on Weil bundles
(Lobachevskii Journal of Mathematics, Volume XVII)
In the present paper, we construct complete lifts of covariant and contravariant tensor fields from the smooth manifold M to its Weil bundle T AM for the case of a Frobenius Weil algebra A. For a Poisson manifold (M,w) we show that the complete lift wC of a Poisson tensor w is again a Poisson tensor on T AM and that wC is a linear combination of some "basic" Poisson structures on T AM induced by w. Finally, we introduce the notion of a weakly symmetric Frobenius Weil algebra A and we compute the modular class of (T AM, wC) for such algebras.