Tangent lifts of Poisson and related structures. (English) Zbl 0872.58028

Grabowski, J.; Urbański, P.

J. Phys. A, Math. Gen. 28, No. 23, 6743-6777 (1995).

Summary: The derivation \(d_T\) on the exterior algebra of forms on a manifold \(M\) with values in the exterior algebra of forms on the tangent bundle \(TM\) is extended to multivector fields. These tangent lifts are studied with application to the theory of Poisson structures, their symplectic foliations, canonical vector fields and Poisson-Lie groups.

MSC:

37J99	Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
58A15	Exterior differential systems (Cartan theory)

Keywords:

multivector fields; tangent lifts; Poisson structures; symplectic foliations; canonical vector fields; Poisson-Lie groups