  In this work we introduce an obstruction for the existence of symplectic
structures on nilpotent Lie algebras. Indeed, a necessary condition is
presented in terms of the cohomology of the Lie algebra. Using this obstruction
we obtain both positive and negative results on the existence of symplectic
structures on a large family of nilpotent Lie algebras. Namely the family of
nilradicals of minimal parabolic subalgebras associated to the real split Lie
algebra of classical complex simple Lie algebras.
