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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

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

buildings, Lie algebras, extremal elements, symplectic geometries
Mathematical Subject Classification
Primary: 16W10, 17B60, 51A50, 51E24
Secondary: 51A45
Received: 13 July 2022
Revised: 31 July 2023
Accepted: 17 August 2023
Published: 13 September 2023
Hans Cuypers
Department of Mathematics and Computing Science
Eindhoven University of Technology
Yael Fleischmann
Department of Mathematical Sciences
Norwegian University of Science and Technology NTNU