On nilpotent generators of the symplectic Lie algebra

Abstract

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 ${\mathfrak{sp}}_{2n}(\mathbb{K})$.

5 pages