In the present paper, we construct complete lifts of covariant and contravariant tensor fields from the smooth manifold M to its Weil bundle TA M for the case of a Frobenius Weil algebraA. For a Poisson manifold (M,w) we show that the complete lift wC of a Poisson tensor w is again a Poisson tensor on TA M and that wC is a linear combination of some "basic" Poisson structures on TA M induced byw. Finally, we introduce the notion of a weakly symmetric Frobenius Weil algebra A and we compute the modular class of (TA M, wC) for such algebras.
DVI format ( 147 Kb), ZIP-ed DVI format ( 51 Kb),
ZIP-ed PostScript format ( 222 Kb), ZIP-ed PDF format (195 Kb )