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Ree geometries

Fabienne Haot, Koen Struyve and Hendrik Van Maldeghem UGent (2011) FORUM MATHEMATICUM. 23(1). p.75-98
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Moufang sets, Ree groups, Ree unital, mixed hexagons
journal title
FORUM MATHEMATICUM
Forum Math.
volume
23
issue
1
pages
75 - 98
Web of Science type
Article
Web of Science id
000286871600002
JCR category
MATHEMATICS
JCR impact factor
0.607 (2011)
JCR rank
129/288 (2011)
JCR quartile
2 (2011)
ISSN
0933-7741
DOI
10.1515/FORM.2011.002
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1199274
handle
http://hdl.handle.net/1854/LU-1199274
date created
2011-03-30 13:05:17
date last changed
2016-12-19 15:45:53
@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},
  keyword      = {Moufang sets,Ree groups,Ree unital,mixed hexagons},
  language     = {eng},
  number       = {1},
  pages        = {75--98},
  title        = {Ree geometries},
  url          = {http://dx.doi.org/10.1515/FORM.2011.002},
  volume       = {23},
  year         = {2011},
}

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.