A geometric characterization of the symplectic Lie algebra

Hans Cuypers, Yael Fleischmann

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We provide a characterization of symplectic Lie algebras over fields of characteris-tic ≠ 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.

Original languageEnglish
Pages (from-to)223-245
Number of pages23
JournalInnovations in Incidence Geometry
Volume20
Issue number2-3
DOIs
Publication statusPublished - 2023

Funding

This work was done while Fleischmann held a Ph.D. position at the Eindhoven University of Technology. It was part of the research program “Special elements in Lie Algebras” (613.000.905), which was (partly) financed by the Dutch Research Council (NWO). This work was done while Fleischmann held a Ph.D. position at the Eindhoven University of Technology. It was part of the research program “Special elements in Lie Algebras” (613.000.905), which was (partly) financed by the Dutch Research Council (NWO). MSC2020: primary 16W10, 17B60, 51A50, 51E24; secondary 51A45. Keywords: buildings, Lie algebras, extremal elements, symplectic geometries.

FundersFunder number
Eindhoven University of Technology613.000.905
Nederlandse Organisatie voor Wetenschappelijk Onderzoek

    Keywords

    • buildings
    • extremal elements
    • Lie algebras
    • symplectic geometries

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