Symplectic structures on quadratic Lie algebras

Bajo, I.; Benayadi, S.; Medina, A.

Symplectic structures on quadratic Lie algebras

Authors

Bajo, I.

Benayadi, S.

Medina, A.

Description

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 algebra admitting an invertiblederivation 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 classification in terms of symplectic quadratic double extensions.