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Geometric and holomorphic structure of $\mathbb{C} \rtimes \mathbb{C} \setminus \{ 0 \}$
Put $G= \mathbb{C} \rtimes_{\phi} \mathbb{C} \setminus \{0\}$ where $\phi_{a} (z)= az$ for $a \in \mathbb{C} \setminus \{0\}$.
$G$ is a real $4$ dimensional Lie group; then it has a unique left ...
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