is there a classical lie group acting transitively on a corona the title is quite self-explaining. Let's take a corona $\\{z\in\mathbb{C},r<\mid z\mid<R\\}$, for two strictly positive reals $r,R$. I am looking for a "classical" lie group that acts holomorphically transitively on the corona. And if not, a non classical will do the stuff;) I thought of a subgroup of the isometries of the unit disk in the poincaré model, but I think there can not be any of this sort.

For a continuous action, the answer is yes: $\mathbb{C}-\\{0\\}=\mathrm{GL}(1,\mathbb{C})$ is a classical Lie group which acts transitively on itself by multiplication. Now use that $\\{z\in\mathbb{C}:r<|z|
For a holomorphic action, the answer is no: If $f$ is a biholomorphism of the annuli, then either $|f(z)|=|z|$ for all $z$ or $|f(z)|=Rr/|z|$ for all $z$ (assuming $0