A geometric characterization of the symplectic Lie algebra

H. Cuypers, Y. Fleischmann

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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 languageEnglish
Article number1707.02095
Number of pages28
JournalarXiv
Volume2017
Publication statusPublished - 7 Jul 2017

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