Résumé
We study quadratic Lie algebras over a field
K
of null characteristic which admit, at the same time, a symplectic structure. We see that if
K
is algebraically closed every such Lie algebra may be constructed as the
T
∗
-extension of a nilpotent Lie algebra admitting an invertible derivation and also as the double extension of another quadratic symplectic Lie algebra by the one-dimensional Lie algebra. Finally, we prove that every symplectic quadratic Lie algebra is a special symplectic Manin algebra and we give an inductive description in terms of symplectic quadratic double extensions.