# Differentiable Manifolds/Lie groups

A Lie group is a differentiable manifold ${\displaystyle G}$ whose group law (denoted here by juxtaposition) has the following properties:
1. The function ${\displaystyle G\times G\to G}$, ${\displaystyle (g,h)\mapsto gh}$ is differentiable
2. The function ${\displaystyle G\to G}$, ${\displaystyle h\mapsto h^{-1}}$ is differentiable