Polarities of Exceptional Geometries of Type E 6

Vincent Batens and Hendrik Van Maldeghem ()
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Vincent Batens: Department of Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 299-S9, B-9000 Ghent, Belgium
Hendrik Van Maldeghem: Department of Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 299-S9, B-9000 Ghent, Belgium

Mathematics, 2025, vol. 13, issue 23, 1-27

Abstract: A polarity of an exceptional geometry of type E 6 is called regularif its fixed structure, viewed as a simplicial complex, is a building. Polarities that do not act trivially on the underlying field were classified a long time ago by Jacques Tits. In the present paper, we classify the regular polarities of exceptional geometries of type E 6 that act trivially on the underlying (arbitrary) field. As a result, we discover new subgeometries of the exceptional geometry of type E 6 .

Keywords: spherical buildings; duality; exceptional type E 6; polarities; generalised quadrangles; metasymplectic space; absolute points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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