An Integrability Criterion for Banach-Lie Triple Systems

Details An Integrability Criterion for Banach-Lie Triple Systems An Integrability Criterion for Banach-Lie Triple Systems

2010-10-22

arxiv.org/abs/1010.4632v3

Journal of Lie Theory 22 (2012), No. 1, 205--244

Mathematics

Differential Geometry

36 pages; linguistic corrections. arXiv admin note: substantial text overlap with arXiv:1010.4427

Scientific paper

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.

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