Hamiltonian BRST deformation of a class of n-dimensional BF-type theories

Consistent Hamiltonian interactions that can be added to an abelian free BF-type class of theories in any n geq 4 spacetime dimensions are constructed in the framework of the Hamiltonian BRST deformation based on cohomological techniques. The resulting model is an interacting field theory in higher dimensions with an open algebra of on-shell reducible first-class constraints. We argue that the Hamiltonian couplings are related to a natural structure of Poisson manifold on the target space.