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.
V. Del Barco (Wed,) studied this question.
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