On the manifold of tripotents in JB ∗-triples

• Published in: Journal of mathematical analysis and applications Vol. 304; no. 1; pp. 147 - 157
• Main Authors: Isidro, José M., Stachó, László L.
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.04.2005; Elsevier
• Subjects: Banach–Lie algebras and groups; Cartan factors; Differential geometry; Exact sciences and technology; Geometry; Global analysis, analysis on manifolds; Grassmann manifolds; JB ∗-triples; Manifolds and cell complexes; Mathematical analysis; Mathematics; Riemann manifolds; Sciences and techniques of general use; Several complex variables and analytic spaces; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Banach–Lie algebras and groups; JB ∗-triples; Cartan factors; Grassmann manifolds; Riemann manifolds; Cartan factor; JB triple; Group algebra; Kähler manifold; Necessary and sufficient condition; Fiber space; JB-triples; Banach-Lie algebras and groups; Riemann manifold; Banach algebra; Grassmann manifold; Equivalence; Mathematical analysis; Symmetric space; Geodesic; Lie group; Lie algebra
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2004.09.009

The manifold of tripotents in an arbitrary JB*-triple Z is considered, a natural affine connection is defined on it in terms of the Peirce projections of Z, and a precise description of its geodesics is given. Regarding this manifold as a fiber space by Neher's equivalence, the base space is a symmetric Kähler manifold when Z is a classical Cartan factor, and necessary and sufficient conditions are established for connected components of the manifold to admit a Riemann structure.