Projective Completions of Jordan Pairs, Part II: Manifold Structures and Symmetric Spaces

Bertram W, Neeb KH (2005)

Publication Type: Journal article, Original article

Publication year: 2005

Journal

Geometriae Dedicata Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 112

Pages Range: 75-115

Journal Issue: 1

DOI: 10.1007/s10711-004-4197-6

Abstract

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.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

Université de Lorraine

France (FR)

How to cite

APA:

Bertram, W., & Neeb, K.H. (2005). Projective Completions of Jordan Pairs, Part II: Manifold Structures and Symmetric Spaces. Geometriae Dedicata, 112(1), 75-115. https://doi.org/10.1007/s10711-004-4197-6

MLA:

Bertram, Wolfgang, and Karl Hermann Neeb. "Projective Completions of Jordan Pairs, Part II: Manifold Structures and Symmetric Spaces." Geometriae Dedicata 112.1 (2005): 75-115.

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