In geometry, a complex Lie group is a Lie group over the complex numbers; i.e., it is a complex-analytic manifold that is also a group in such a way G × G → G , ( x , y ) ↦ x y − 1 {\displaystyle G\times G\to G,(x,y)\mapsto xy^{-1}} is holomorphic. Basic examples are GL n ( C ) {\displaystyle \operatorname {GL} _{n}(\mathbb {C} )} , the general linear groups over the complex numbers.
In geometry, a complex Lie group is a Lie group over the complex numbers; i.e., it is a complex-analytic manifold that is also a group in such a way G × G → G , ( x , y ) ↦ x y − 1 {\displaystyle G\times G\to G,(x,y)\mapsto xy^{-1}} is holomorphic. Basic examples are GL n ( C ) {\displaystyle \operatorname {GL} _{n}(\mathbb {C} )} , the general linear groups over the complex numbers.
Source: Wikipedia "Complex Lie group" · CC BY-SA 4.0
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