Un théorème de Liouville pour les algèbres de Jordan
The geometry of null systems, Jordan algebras and von Staudt's theorem
We characterize an important class of generalized projective geometries by the following essentially equivalent properties: (1) admits a central null-system; (2) admits inner polarities: (3) 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...
Jordan- and Lie geometries
In these lecture notes we report on research aiming at understanding the relation beween algebras and geometries, by focusing on the classes of Jordan algebraic and of associative structures and comparing them with Lie structures. The geometric object sought for, called a generalized projective, resp. an associative geometry, can be seen as a combination of the structure of a symmetric space, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic...
Hardy spaces and analytic continuation of Bergman spaces
On some causal and conformal groups.
Generalized projective geometries: General theory and equivalance with Jordan structures.
Characterization of the Kantor-Koecher-Tits algebra by a generalized Ahlfors operator.
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