  We construct a large family of evidently integrable Hamiltonian systems which
are generalizations of the KM system. The Hamiltonian vector field is
homogeneous cubic but in a number of cases a simple change of variables
transforms such a system to a quadratic Lotka-Volterra system. We present in
detail all such systems in dimensions 4 and 5 and we also give some examples
from higher dimensions. This construction generalizes easily to each complex
simple Lie algebra.
