Abstract
A nonzero element $x$ in a Lie algebra $\mathfrak{g}$ with Lie product $[ , ]$ is called extremal if $[x,[x,y]]$ is a multiple of $x$ for all $y$. In this paper we characterize the (finitary) symplectic Lie algebras as simple Lie algebras generated by their extremal elements satisying the condition that any two noncommuting extremal elements $x,y$ generate an $\mathfrak{sl}_2$ and any third extremal element $z$ commutes with at least one extremal element in this $\mathfrak{sl}_2$.
| Original language | English |
|---|---|
| Article number | 1707.02095 |
| Number of pages | 28 |
| Journal | arXiv |
| Volume | 2017 |
| Publication status | Published - 7 Jul 2017 |
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Cuypers, H., & Fleischmann, Y. (2017). A geometric characterization of the symplectic Lie algebra. arXiv, 2017, [1707.02095]. https://arxiv.org/abs/1707.02095