English

Quadrangles embedded in metasymplectic spaces

Combinatorics 2009-09-29 v1

Abstract

During the final steps in the classification of the Moufang quadrangles by Jacques Tits and Richard Weiss a new class of Moufang quadrangles unexpectedly turned up. Subsequently Bernhard Muhlherr and Hendrik Van Maldeghem showed that this class arises as the fixed points and hyperlines of certain involutions of a metasymplectic space (or equivalently a building of type F_4). In the same paper they also showed that other types of Moufang quadrangles can be embedded in a metasymplectic space as points and hyperlines. In this paper, we reverse the question: given a (thick) quadrangle embedded in a metasymplectic space as points and hyperlines, when is such a quadrangle a Moufang quadrangle?

Cite

@article{arxiv.0909.4960,
  title  = {Quadrangles embedded in metasymplectic spaces},
  author = {Koen Struyve},
  journal= {arXiv preprint arXiv:0909.4960},
  year   = {2009}
}
R2 v1 2026-06-21T13:51:08.712Z