  A new family of skew-symmetric solutions of the Jacobi partial differential
equations for finite-dimensional Poisson systems is characterized and analyzed.
Such family has some remarkable properties. In first place, it is defined for
arbitrary values of the dimension and the rank. Secondly, it is described in
terms of arbitrary differentiable functions, namely it is not limited to a
given degree of nonlinearity. Additionally, it is possible to determine
explicitly the fundamental properties of those solutions, such as their Casimir
invariants and the algorithm for the reduction to the Darboux canonical form,
which have been reported only for a very limited sample of finite-dimensional
Poisson structures. Moreover, such analysis is carried out globally in phase
space, thus improving the usual local scope of Darboux theorem.
