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Symplectic structures on quadratic Lie algebras

I. Bajo·S. Benayadi·A. Medina
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Abstract

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.

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I. Bajo, S. Benayadi, A. Medina. 2006-03-03. Symplectic structures on quadratic Lie algebras. https://arxiv.org/abs/math/0603066

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