On Exceptional Lie Geometries

Abstract

Parapolar spaces are point-line geometries introduced as a geometric approach to (exceptional) algebraic groups. We provide a characterization of a wide class of Lie geometries as parapolar spaces satisfying a simple intersection property. In particular many of the exceptional Lie geometries occur. In fact, our approach unifies and extends several earlier characterizations of (exceptional) Lie geometries arising from spherical Tits-buildings.

This is joint work with Anneleen De Schepper, Hendrik Van Maldeghem and Magali Victoor.