J. Grabowski et P. Urbanski, TANGENT LIFTS OF POISSON AND RELATED STRUCTURES, Journal of physics. A, mathematical and general, 28(23), 1995, pp. 6743-6777
The derivation dr on the exterior algebra of forms on a manifold M wit
h values in the exterior algebra of forms on the tangent bundle T M is
extended to multivector fields. These tangent lifts are studied with
application to the theory of Poisson structures, their symplectic foli
ations, canonical vector fields and Poisson-Lie groups.