Journal of Lie Theory 22 (2012), No. 1, 205--244
Copyright Heldermann Verlag 2012
An Integrability Criterion for Banach-Lie Triple Systems
Michael Klotz
Technische Universität, Schlossgartenstr. 7, 64289 Darmstadt, Germany
klotz@mathematik.tu-darmstadt.de
To give a criterion for the integrability of Banach-Lie triple systems, we follow the construction of the period group of a Lie algebra and define the period group of a Lie triple system as an analogous concept. We show that a Lie triple system is integrable if and only if its period group is discrete. Along the way, we see how to turn the path and the loop space of a pointed symmetric space into pointed symmetric spaces.
Keywords: Banach symmetric space, Lie triple system, period group, path space.
MSC: 53C35, 22E65
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