  This work is devoted to the establishment of a Poisson structure for a format
of equations known as Generalized Lotka-Volterra systems. These equations,
which include the classical Lotka-Volterra systems as a particular case, have
been deeply studied in the literature. They have been shown to constitute a
whole hierarchy of systems, the characterization of which is made in the
context of simple algebra. Our main result is to show that this algebraic
structure is completely translatable into the Poisson domain. Important Poisson
structures features, such as the symplectic foliation and the Darboux'
canonical representation, arise as result of rather simple matrix
manipulations.
