Geometries, the principle of duality, and algebraic groups
arXiv:math/0503201 · doi:10.1016/j.exmath.2005.11.001
Abstract
Jacques Tits gave a general recipe for producing an abstract geometry from a semisimple algebraic group. This expository paper describes a uniform method for giving a concrete realization of Tits's geometry and works through several examples. We also give a criterion for recognizing the automorphism of the geometry induced by an automorphism of the group. The E6 geometry is studied in depth.
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