Complex Lie group

In geometry, a complex Lie group is a complex-analytic manifold that is also a group in such a way $G \times G \to G, (x, y) \mapsto x y^{-1}$ is holomorphic. Basic examples are $\operatorname{GL}_n(\mathbb{C})$ , the general linear groups over the complex numbers. A connected compact complex Lie group is precisely a complex torus (not to be confused with the complex Lie group $\mathbb C^*$ ). Any finite group may be given the structure of a complex Lie group. A complex semisimple Lie group is an algebraic group.

单词	Complex Lie group
释义	Complex Lie group 英语百科 Complex Lie group In geometry, a complex Lie group is a complex-analytic manifold that is also a group in such a way $G \times G \to G, (x, y) \mapsto x y^{-1}$ is holomorphic. Basic examples are $\operatorname{GL}_n(\mathbb{C})$ , the general linear groups over the complex numbers. A connected compact complex Lie group is precisely a complex torus (not to be confused with the complex Lie group $\mathbb C^*$ ). Any finite group may be given the structure of a complex Lie group. A complex semisimple Lie group is an algebraic group.
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