On nilpotent generators of the symplectic Lie algebra


Abstract in English

Let $mathfrak{sp}_{2n}(mathbb {K})$ be the symplectic Lie algebra over an algebraically closed field of characteristic zero. We prove that for any nonzero nilpotent element $X in mathfrak{sp}_{2n}(mathbb {K})$ there exists a nilpotent element $Y in mathfrak{sp}_{2n}(mathbb {K})$ such that $X$ and $Y$ generate $mathfrak{sp}_{2n}(mathbb {K})$.

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