## Vadim V. Shurygin, junior

# Poisson structures on Weil bundles

## (Lobachevskii Journal of Mathematics, Vol.17, pp.229 - 256)

In the present paper, we construct complete lifts
of covariant and
contravariant tensor fields from the smooth
manifold M to its Weil
bundle T^{A} M for the case of a
Frobenius Weil algebraA.
For a Poisson manifold (M,w) we show that the complete lift w^{C}
of a Poisson tensor w is again a Poisson tensor on T^{A} M and that
w^{C} is a linear combination of some "basic" Poisson structures on
T^{A} M induced byw.
Finally, we introduce the notion of a weakly symmetric Frobenius
Weil algebra A and we compute the modular class of (T^{A} M, w^{C})
for such algebras.

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