The Campbell- Hausdorff Series of Local Analytic Bruck Loops

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The class of local analyitic Bruck loops (or equivalently K-loops) is strongly related to locally symmetric spaces. In particular, both have Lie triple systems as their tangent algebra. In this paper, we consider the existence and some properties of the Campbell-Hausdorff series of local analytic Bruck loops (K-loops). This formula can be used to determine the local symmetries of the associated symmetric space.

Supported by the Hungarian Eötvös State Fellowship, by the FKFP grant 0063/2001 and the OTKA grant F030737. In part, this paper was written when the author was a research assistant in the Mathematisches Institut der Universität Erlangen-Nürnberg. © Mathematisches Seminar der Universität Hamburg, 2002