Nilradicals of parabolic subalgebras admitting symplectic structures (Q268421)

Let \(R\) be the real number field. Finite dimensional real Lie algebras which admit a symplectic structure are considered in this paper. The algebras are nil radicals of parabolic subalgebras of a Lie algebra. In particular, if \(N\) is such a nil radical and either \(N\) or the direct sum of \(R\) and \(N\) admit a symplectic structure, then \(N\) is one of seven types of Lie algebras.