  We answer a question of Oprea-Tralle on the realizability of symplectic
algebras by symplectic manifolds in dimensions divisible by four, along with a
question of Lupton-Oprea in all even dimensions. This will also allow us to
address, in all even dimensions six and higher, another question of
Oprea-Tralle on the possibility of algebraic conditions on the rational
homotopy minimal model of a closed smooth manifold implying the existence of a
symplectic structure on the manifold.
