Lie group

A Lie group is a topological group on an analytic manifold such that the group operation and the inverse map are analytic. #m/def/lie Equivalently, the map is analytic.

Charts and atlases of a Lie group

Due to properties of a Lie group as a Homogenous space, it is possible to build an atlas for the entire group from a single coördinate chart . For if is a chart with , then may be defined as

so that .

Every Lie group has a corresponding Lie algebra given by the Tangent space at identity. #to/clarify

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