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A geometric characterization of the symplectic Lie algebra

Hans Cuypers and Yael Fleischmann

Vol. 20 (2023), No. 2-3, 223–245
Abstract

We provide a characterization of symplectic Lie algebras over fields of characteristic 2 as Lie algebras generated by extremal elements in which any two extremal elements x and y either commute or generate an 𝔰𝔩2, and for any three extremal elements x,y,z in 𝔤 with [x,y]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