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arXiv · 1605.07758

On the radicals of exponential Lie groups

S. G. Dani
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Abstract

Let $G$ be a connected exponential Lie group and $R$ be the solvable radical of $G$. We describe a condition on $G/R$ under which one can then conclude that $R$ is an exponential Lie group. The condition holds in particular when $G$ is a complex Lie group and this yields a stronger version of a result of Moskowitz and Sacksteder \cite{MS} on the center of a complex exponential Lie group being connected. Along the way we prove a criterion for elements from certain subsets of a solvable Lie group to be exponential, which would be of independent interest.

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S. G. Dani. 2016-05-25. On the radicals of exponential Lie groups. https://arxiv.org/abs/1605.07758

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