On exceptional Lie geometries
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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2021-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509420000572/type/journal_article |
| _version_ | 1811156210750062592 |
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| author | Anneleen De Schepper Jeroen Schillewaert Hendrik Van Maldeghem Magali Victoor |
| author_facet | Anneleen De Schepper Jeroen Schillewaert Hendrik Van Maldeghem Magali Victoor |
| author_sort | Anneleen De Schepper |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T04:47:43Z |
| format | Article |
| id | doaj.art-ea655dd3eca3452f8c99a94a1357e01b |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:43Z |
| publishDate | 2021-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-ea655dd3eca3452f8c99a94a1357e01b2023-03-09T12:34:52ZengCambridge University PressForum of Mathematics, Sigma2050-50942021-01-01910.1017/fms.2020.57On exceptional Lie geometriesAnneleen De Schepper0Jeroen Schillewaert1Hendrik Van Maldeghem2Magali Victoor3Department of Mathematics, Ghent University, 9000 Ghent Belgium; E-mail: .Department of Mathematics, University of Auckland, 1010 Auckland New Zealand; E-mail: .Department of Mathematics, Ghent University, 9000 Ghent Belgium; E-mail: .Department of Mathematics, Ghent University, 9000 Ghent Belgium; E-mail: .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.https://www.cambridge.org/core/product/identifier/S2050509420000572/type/journal_article51E2451B2520E42 |
| spellingShingle | Anneleen De Schepper Jeroen Schillewaert Hendrik Van Maldeghem Magali Victoor On exceptional Lie geometries Forum of Mathematics, Sigma 51E24 51B25 20E42 |
| title | On exceptional Lie geometries |
| title_full | On exceptional Lie geometries |
| title_fullStr | On exceptional Lie geometries |
| title_full_unstemmed | On exceptional Lie geometries |
| title_short | On exceptional Lie geometries |
| title_sort | on exceptional lie geometries |
| topic | 51E24 51B25 20E42 |
| url | https://www.cambridge.org/core/product/identifier/S2050509420000572/type/journal_article |
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