## 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 sl_{2}, 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 language | English |
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Pages (from-to) | 223-245 |

Number of pages | 23 |

Journal | Innovations in Incidence Geometry |

Volume | 20 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 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.

Funders | Funder number |
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Eindhoven University of Technology | 613.000.905 |

Nederlandse Organisatie voor Wetenschappelijk Onderzoek |

## Keywords

- buildings
- extremal elements
- Lie algebras
- symplectic geometries