
Journal of Lie Theory 22 (2012), No. 1, 205244 Copyright Heldermann Verlag 2012 An Integrability Criterion for BanachLie Triple Systems Michael Klotz Technische Universität, Schlossgartenstr. 7, 64289 Darmstadt, Germany klotz@mathematik.tudarmstadt.de To give a criterion for the integrability of BanachLie 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 [ Fulltextpdf (523 KB)] for subscribers only. 