Complex Lie group

Definition
A complex Lie group is a set equipped with two structures:


 * The structure of a group, viz a binary operation called multiplication or product, a unary operation called the inverse map, and a constant called the identity element
 * The structure of a complex manifold

in such a manner that:


 * The group multiplication operation is a complex-analytic map from the direct product of the group with itself (with the product manifold structure)
 * The inverse map is a complex-analytic map from the group to itself