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Article Dans Une Revue Geometriae Dedicata Année : 2005

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.
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Dates et versions

hal-00102108 , version 1 (29-09-2006)

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  • HAL Id : hal-00102108 , version 1

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Wolfgang Bertram, Karl-Hermann Neeb. Projective completions of jordan pair. Part II : manifold structures and symmetric spaces. Geometriae Dedicata, 2005, 112 (1), pp.73-113. ⟨hal-00102108⟩
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