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# Regular Embeddings of Generalized Hexagons

Published:2004-10-01
Printed: Oct 2004
• Anja Steinbach
• Hendrik Van Maldeghem
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## Abstract

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 $\ssG_2$, $^3\ssD_4$ and $^6\ssD_4$ (and occurring in projective dimensions $5,6,7$), we find new examples in unbounded dimension related to the mixed groups of type $\ssG_2$.
 Keywords: Moufang generalized hexagons, embeddings, mixed hexagons, classical, hexagons
 MSC Classifications: 51E12 - Generalized quadrangles, generalized polygons 51A45 - Incidence structures imbeddable into projective geometries