Projective completions of Jordan pairs Part II. Manifold structures and symmetric spaces

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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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Group Theory, Differential Geometry, 17C36, 46H70, 17C65, 17C30, 17C90

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http://salesiana.dossiersoluciones.com/handle/123456789/69893

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0401236
 http://arxiv.org/abs/math/0401236

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arXiv