- Author
- Vincent Batens (UGent) and Hendrik Van Maldeghem (UGent)
- Organization
- Project
- Abstract
- A polarity of an exceptional geometry of type E-6 is called regularif its fixed structure, viewed as a simplicial complex, is a building. Polarities that do not act trivially on the underlying field were classified a long time ago by Jacques Tits. In the present paper, we classify the regular polarities of exceptional geometries of type E-6 that act trivially on the underlying (arbitrary) field. As a result, we discover new subgeometries of the exceptional geometry of type E-6.
- Keywords
- spherical buildings, duality, exceptional type 𝖤6, polarities, generalised quadrangles, metasymplectic space, absolute points
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01KEYNFA6CNSVT8EX5T1H572H0
- MLA
- Batens, Vincent, and Hendrik Van Maldeghem. “Polarities of Exceptional Geometries of Type E6.” MATHEMATICS, vol. 13, no. 23, MDPI AG, 2025, doi:10.3390/math13233804.
- APA
- Batens, V., & Van Maldeghem, H. (2025). Polarities of exceptional geometries of type E6. MATHEMATICS, 13(23). https://doi.org/10.3390/math13233804
- Chicago author-date
- Batens, Vincent, and Hendrik Van Maldeghem. 2025. “Polarities of Exceptional Geometries of Type E6.” MATHEMATICS 13 (23). https://doi.org/10.3390/math13233804.
- Chicago author-date (all authors)
- Batens, Vincent, and Hendrik Van Maldeghem. 2025. “Polarities of Exceptional Geometries of Type E6.” MATHEMATICS 13 (23). doi:10.3390/math13233804.
- Vancouver
- 1.Batens V, Van Maldeghem H. Polarities of exceptional geometries of type E6. MATHEMATICS. 2025;13(23).
- IEEE
- [1]V. Batens and H. Van Maldeghem, “Polarities of exceptional geometries of type E6,” MATHEMATICS, vol. 13, no. 23, 2025.
@article{01KEYNFA6CNSVT8EX5T1H572H0,
abstract = {{A polarity of an exceptional geometry of type E-6 is called regularif its fixed structure, viewed as a simplicial complex, is a building. Polarities that do not act trivially on the underlying field were classified a long time ago by Jacques Tits. In the present paper, we classify the regular polarities of exceptional geometries of type E-6 that act trivially on the underlying (arbitrary) field. As a result, we discover new subgeometries of the exceptional geometry of type E-6.}},
articleno = {{3804}},
author = {{Batens, Vincent and Van Maldeghem, Hendrik}},
issn = {{2227-7390}},
journal = {{MATHEMATICS}},
keywords = {{spherical buildings,duality,exceptional type 𝖤6,polarities,generalised quadrangles,metasymplectic space,absolute points}},
language = {{eng}},
number = {{23}},
pages = {{27}},
publisher = {{MDPI AG}},
title = {{Polarities of exceptional geometries of type E6}},
url = {{http://doi.org/10.3390/math13233804}},
volume = {{13}},
year = {{2025}},
}
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