Metric Lie groups admitting dilations
Metric Lie groups admitting dilations
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, ∞)→Aut(G), λ →δ λ , so that d(δ λ x, δ λ y)=λd(x, y), for all x, y∈G and all λ>0.First, we show that all such …