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# Are $C, C^*$ and $T$ the only 1-diemensional complex Lie groups?
I'm aware that there is a classification of certain kinds of complex Lie groups like semisimple or compact. Is there a classification of the Lie groups in the 1-dimensional case? It seems to me that the only Lie groups are the complex plane ${\mathbb{C}}$, the multiplicative group of nonzero complex numbers ${\mathbb{C}}^*$ and the torus ${\mathbb{T}}$.