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Regular Embeddings of Generalized Hexagons

Published online by Cambridge University Press:  20 November 2018

Anja Steinbach  and
Hendrik Van Maldeghem
Anja Steinbach
Affiliation:
Justus-Liebig-Universität Gießen, Mathematisches Institut, Arndtstraße 2, D 35392 Gießen, Germany e-mail: Anja.Steinbach@math.uni-giessen.de
Hendrik Van Maldeghem
Affiliation:
Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Gent, Belgium e-mail: hvm@cage.rug.ac.be
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Abstract

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We classify the generalized hexagons which are laxly embedded in projective space such that the embedding is flat and polarized. Besides the standard examples related to the hexagons defined over the algebraic groups of type ${{\text{G}}_{2}}$, ${}^{3}{{\text{D}}_{4}}$ and ${}^{6}{{\text{D}}_{\text{4}}}$ (and occurring in projective dimensions 5, 6, 7), we find new examples in unbounded dimension related to the mixed groups of type ${{\text{G}}_{2}}$ .

Keywords

51E1251A45Moufang generalized hexagonsembeddingsmixed hexagonsclassical hexagons
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 5 , 01 October 2004 , pp. 1068 - 1093
Copyright
Copyright © Canadian Mathematical Society 2004

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