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

We characterize an important class of generalized projective geometries (see preprints 89 and 90 on this server) by the following equivalent properties:

(1) the geometry admits a central null-system,

(2) the geometry admits inner polarities,

(3) the geometry is associated to a unital Jordan algebra.

Such geometries, called "of the first kind", play in the category of generalized projective geometries a role comparable to that of the projective line in the category of ordinary projective geometries. In this general set-up, we prove an analogue of von Staudt's theorem which generalizes similar results by L. K. Hua.

(This paper has appeared in Ann. Inst. Fourier t. 53, fasc. 1 (2003), 193--225)

null.dvi (132K)

W. Bertram < bertram@iecn.u-nancy.fr >