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On exceptional Lie geometries

Part of: Nonlinear incidence geometry Finite geometry and special incidence structures Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  11 January 2021

Anneleen De Schepper ,
Jeroen Schillewaert ,
Hendrik Van Maldeghem  and
Magali Victoor
Anneleen De Schepper
Affiliation:
Department of Mathematics, Ghent University, 9000GhentBelgium; E-mail: anneleen.deschepper@ugent.be.
Jeroen Schillewaert
Affiliation:
Department of Mathematics, University of Auckland, 1010AucklandNew Zealand; E-mail: j.schillewaert@auckland.ac.nz.
Hendrik Van Maldeghem
Affiliation:
Department of Mathematics, Ghent University, 9000GhentBelgium; E-mail: hendrik.vanmaldeghem@ugent.be.
Magali Victoor
Affiliation:
Department of Mathematics, Ghent University, 9000GhentBelgium; E-mail: magali.victoor@ugent.be.

Abstract

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Parapolar spaces are point-line geometries introduced as a geometric approach to (exceptional) algebraic groups. We characterize a wide class of Lie geometries as parapolar spaces satisfying a simple intersection property. In particular, many of the exceptional Lie incidence geometries occur. In an appendix, we extend our result to the locally disconnected case and discuss the locally disconnected case of some other well-known characterizations.

MSC classification

Primary: 51E24: Buildings and the geometry of diagrams
Secondary: 51B25: Lie geometries 20E42: Groups with a $BN$-pair; buildings
Type
Algebra
Information
Forum of Mathematics, Sigma , Volume 9 , 2021 , e2
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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