Abstract

We provide a characterization of symplectic Lie algebras over fields of characteristic $\ne 2$ as Lie algebras generated by extremal elements in which any two extremal elements $x$ and $y$ either commute or generate an ${\mathfrak{𝔰}\mathfrak{𝔩}}_2$, and for any three extremal elements $x,y,z$ in $\mathfrak{𝔤}$ with $[x,y]\ne 0$, there is an extremal $u$ in the subalgebra $⟨x,y⟩$ commuting with $z$.

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