Differentiable Manifolds/Lie groups

< Differentiable Manifolds

Definition (Lie group):

A Lie group is a differentiable manifold $G$ whose group law (denoted here by juxtaposition) has the following properties:

The function $G\times G\to G$ , $(g,h)\mapsto gh$ is differentiable
The function $G\to G$ , $h\mapsto h^{-1}$ is differentiable

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