  In this paper we deal with symplectic Lie algebras. All symplectic structures
are determined for dimension four and the corresponding Lie algebras are
classified up to equivalence. Symplectic four dimensional Lie algebras are
described either as solutions of the cotangent extension problem or as
symplectic double extension of $\Bbb RR^2$ by $\Bbb RR$. The difference in the
choice of a certain model lies on the existence or not of a lagrangian ideal.
Moreover all extensions of a two dimensional Lie algebra are determined, and so
all solutions (up to equivalence) of the cotangent extension problem are given
in dimension two. By studying the adjoint representation we generalize to
higher dimensions finding obstructions to the existence of symplectic forms.
Finally, as an appendix we compute the authomorphisms of four dimensional
symplectic Lie algebras and the cohomology over $\Bbb RR$ of the solvable real
four dimensional Lie algebras.
