A geometric characterization of the symplectic Lie algebra

We provide a characterization of symplectic Lie algebras over fields of characteristic $\neq 2$ as Lie algebras generated by extremal elements in which any two extremal elements $x$ and $y$ either commute or generate an ${𝔰 𝔩}_{2}$ , and for any three extremal elements $x, y, z$ in $𝔤$ with $[x, y] \neq 0$ , there is an extremal $u$ in the subalgebra $⟨ x, y ⟩$ commuting with $z$ .

Dedicated to the memory of Jacques Tits

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Keywords

buildings, Lie algebras, extremal elements, symplectic geometries

Mathematical Subject Classification

Primary: 16W10, 17B60, 51A50, 51E24

Secondary: 51A45

Milestones

Received: 13 July 2022

Revised: 31 July 2023

Accepted: 17 August 2023

Published: 13 September 2023

Authors

Hans Cuypers
Department of Mathematics and Computing Science Eindhoven University of Technology Eindhoven Netherlands

Yael Fleischmann
Department of Mathematical Sciences Norwegian University of Science and Technology NTNU Trondheim Norway

Vol. 20, No. 2-3, 2023

Hans Cuypers and Yael Fleischmann

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors