# Metric Lie groups admitting dilations

@article{Donne2019MetricLG, title={Metric Lie groups admitting dilations}, author={Enrico Le Donne and Sebastiano Golo}, journal={Arkiv f{\"o}r Matematik}, year={2019} }

We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, \infty)\rightarrow\mathtt{Aut}(G)$, $\lambda\mapsto\delta_\lambda$, so that $ d(\delta_\lambda x,\delta_\lambda y) = \lambda d(x,y)$, for all $x,y\in G$ and all $\lambda>0$.
First, we show that all such distances are admissible, that is, they induce the manifold topology. Second, we characterize multiplicative one-parameter groups of Lie…

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