Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 39, No. 1, pp. 37-46 (1998)

On the Exponential Function of Real Splittable and Real Semisimple Lie Groups

Michael Wüstner

Fachbereich Mathematik, Technische Hochschule Darmstadt,
Schlossgartenstrasse 7, D-64289 Darmstadt, Germany

Abstract: A Lie group $G$ is called exponential if its exponential function is surjective. This article contains a characterization of real analytic splittable groups and real semisimple Lie groups with surjective exponential function. It is shown that they are exponential if and only if for each nilpotent element $x$ of the Lie algebra $ L(G)$ the centralizer $Z_G(x)=\{g\in G| Ad(g)(x)=x\}$ is weakly exponential, {i.e.,} has dense exponential image.

Keywords: exponential function; splittable groups; semisimple Lie groups

Classification (MSC91): 22E46

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