Projective completions of jordan pair. Part II : manifold structures and symmetric spaces
Résumé
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields K, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems. This class of spaces, called smooth generalized projective geometries, generalizes the well-known (finite or infinite-dimensional) bounded symmetric domains as well as their ``compact-like'' duals. An interpretation of such geometries as models of Quantum Mechanics is proposed, and particular attention is paid to geometries that might be considered as ``standard models" -- they are associated to associative continuous inverse algebras and to Jordan algebras of hermitian elements in such an algebra.