A geometric characterization of the symplectic Lie algebra

DOI10.2140/iig.2023.20.223arXiv1707.02095MaRDI QIDQ6060076

Yael Fleischmann, Hans Cuypers

Publication date: 2 November 2023

Published in: Innovations in Incidence Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.02095

zbMATH Keywords

Lie algebrasbuildingsextremal elementssymplectic geometries

Mathematics Subject Classification ID

Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Buildings and the geometry of diagrams (51E24) Incidence structures embeddable into projective geometries (51A45) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Polar geometry, symplectic spaces, orthogonal spaces (51A50)

Cites Work

• Recovering the Lie algebra from its extremal geometry
• Extremal presentations for classical Lie algebras
• Extremal elements in Lie algebras, buildings and structurable algebras
• Root shadow spaces
• Simple Lie algebras having extremal elements
• Buildings of spherical type and finite BN-pairs
• Symplectic geometries, transvection groups, and modules
• A geometric characterization of the classical Lie algebras
• On the geometry of inner ideals
• Inner ideals in Lie algebras and spherical buildings
• Root filtration spaces from Lie algebras and abstract root groups
• Point-line characterizations of Lie geometries
• Lie algebras generated by extremal elements.

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