Symplectic Structures on Nilmanifolds: an Obstruction for their Existence

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.