A geometric characterization of the symplectic Lie algebra

2017/07/07 by Hans Cuypers, Cuypers, Hans, Yael Fleischmann +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1707.02095

openalex publication_date 2017/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A nonzero element x in a Lie algebra \mathfrakg 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 \mathfraksl₂ and any third extremal element z commutes with at least one extremal element in this \mathfraksl₂.

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