  First, we review the notion of a Poisson structure on a noncommutative
algebra due to Block-Getzler and Xu and introduce a notion of a Hamiltonian
vector field on a noncommutative Poisson algebra. Then we describe a Poisson
structure on a noncommutative algebra associated with a transversely symplectic
foliation and construct a class of Hamiltonian vector fields associated with
this Poisson structure.
