Polarities of Exceptional Geometries of Type E6

A polarity of an exceptional geometry of type E6 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 E6 that act trivially on the underlying (arbitrary) field. As a result, we discover new subgeometries of the exceptional geometry of type E6.

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Journal
Mathematics
Published
2025-11-27
DOI
https://doi.org/10.3390/math13233804
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
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article

Polarities of Exceptional Geometries of Type E6

Hendrik Van Maldeghem, Vincent Batens
Mathematics
Homotopy and Cohomology in Algebraic Topology
article

Polarities of Exceptional Geometries of Type E6

Hendrik Van Maldeghem, Vincent Batens
article en

Abstract

A polarity of an exceptional geometry of type E6 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 E6 that act trivially on the underlying (arbitrary) field. As a result, we discover new subgeometries of the exceptional geometry of type E6.

MathematicsVol. 13(23)
Ghent University (BE)
Openalex Percentile: Top 57%
Homotopy and Cohomology in Algebraic Topology
DOIOpen Access PDFOpenAlex
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Polarities of Exceptional Geometries of Type E6 — Hendrik Van Maldeghem, Vincent Batens · Mathematics (2025) | TGRS Research Map | TGRS