Abstract
Metasymplectic spaces are geometries representing Tits' weak buildings of Type F 4. For metasymplectic and polar spaces an axiom system is given that characterizes them in terms of points and lines.
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Buekenhout, F.: Les quadriques et leurs généralisations. Lecture Notes Université Libre de Bruxelles, 1978.
Buekenhout, F. and Shult, E. E.: ‘On the Foundations of Polar Geometry.’ Geom. Dedicata 3 (1974), 155–170.
Cameron, P. J.: ‘Flat Embeddings of Near 2n-gons’, in Cameron, Hirschfeld and Hughes (eds.), Finite Geometries and Designs. LMS Lecture Note 49 (Proc. Second Isle of Thorns Conf. 1980), London, 1981.
Cohen, A. M.: ‘Geometries Originating from Certain Distance-Regular Graphs’. in: Cameron, Hirschfeld and Hughes (eds.), Finite Geometries and Designs. LMS Lecture Note, 49, London, 1981.
Cohen, A. M.: ‘On the Points and Lines of Metasymplectic Spaces’ to appear in Proc. Convegno Internazionale Geometrie Combinatorie e loro applicazioni, Rome, 1981.
Cooperstein, B. N.: ‘Some Geometries Associated with Parabolic Representations of Groups of Lie Type’. Can. J. Math. 28 (1976), 1021–1031.
Cooperstein, B. N.: ‘A Characterization of Some Lie Incidence Structures’. Geom. Dedicata 6 (1977), 205–258.
Freudenthal, H.: ‘Beziehungen der E7 und E8 zur Oktavenebene’, I–XI, Proc. Kon. Ned. Akad. Wet. A57 (1954), 218–230, 363–368; A58 (1955), 151–157, 277–285; A62 (1959), 165–201, 447–474; A66 (1963), 457–487 (= Indag. Math., 16, 17, 21, 25).
Shult, E. E. and Yanushka, A.: ‘Near n-gons and Line Systems’, Geom. Dedicata 9 (1980), 1–72.
Tits, J.: Buildings of Spherical Type and Finite BN-pairs, Lecture Notes in Mathematics 386, Springer, 1974.
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Cohen, A.M. An axiom system for metasymplectic spaces. Geom Dedicata 12, 417–433 (1982). https://doi.org/10.1007/BF00147584
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DOI: https://doi.org/10.1007/BF00147584