- Author
- Fabienne Haot, Koen Struyve (UGent) and Hendrik Van Maldeghem (UGent)
- Organization
- Abstract
- We introduce a rank 3 geometry for any Ree group over a not necessarily perfect field and show that its full collineation group is the automorphism group of the corresponding Ree group. A similar result holds for two rank 2 geometries obtained as a truncation of this rank 3 geometry. As an application, we show that a polarity in any Moufang generalized hexagon is unambiguously determined by its set of absolute points, or equivalently, its set of absolute lines.
- Keywords
- Moufang sets, Ree groups, Ree unital, mixed hexagons
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Haot 2011 FM 23 1 75.pdf
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-1199274
- Chicago
- Haot, Fabienne, Koen Struyve, and Hendrik Van Maldeghem. 2011. “Ree Geometries.” Forum Mathematicum 23 (1): 75–98.
- APA
- Haot, F., Struyve, K., & Van Maldeghem, H. (2011). Ree geometries. FORUM MATHEMATICUM, 23(1), 75–98.
- Vancouver
- 1.Haot F, Struyve K, Van Maldeghem H. Ree geometries. FORUM MATHEMATICUM. 2011;23(1):75–98.
- MLA
- Haot, Fabienne, Koen Struyve, and Hendrik Van Maldeghem. “Ree Geometries.” FORUM MATHEMATICUM 23.1 (2011): 75–98. Print.
@article{1199274, abstract = {We introduce a rank 3 geometry for any Ree group over a not necessarily perfect field and show that its full collineation group is the automorphism group of the corresponding Ree group. A similar result holds for two rank 2 geometries obtained as a truncation of this rank 3 geometry. As an application, we show that a polarity in any Moufang generalized hexagon is unambiguously determined by its set of absolute points, or equivalently, its set of absolute lines.}, author = {Haot, Fabienne and Struyve, Koen and Van Maldeghem, Hendrik}, issn = {0933-7741}, journal = {FORUM MATHEMATICUM}, language = {eng}, number = {1}, pages = {75--98}, title = {Ree geometries}, url = {http://dx.doi.org/10.1515/FORM.2011.002}, volume = {23}, year = {2011}, }
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