Every nonzero nilpotent element of the symplectic Lie algebra has a nilpotent companion generating the whole algebra with it.
2-generation of simple Lie algebras a nd free dense subgroups of algebraic groups
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On nilpotent generators of the symplectic Lie algebra
Every nonzero nilpotent element of the symplectic Lie algebra has a nilpotent companion generating the whole algebra with it.