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The geometry of null systems, Jordan algebras and von Staudt's theorem

Wolfgang Bertram (2003)

Annales de l’institut Fourier

We characterize an important class of generalized projective geometries ( X , X ' ) by the following essentially equivalent properties: (1) ( X , X ' ) admits a central null-system; (2) ( X , X ' ) admits inner polarities: (3) ( X , X ' ) is associated to a unital Jordan algebra. These geometries, called of the first kind, play in the category of generalized projective geometries a rôle comparable to the one of the projective line in the category of ordinary projective geometries. In this general set-up, we prove an analogue of von Staudt’s...

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