Vadim V. Shurygin, junior

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.
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