Definitions and Examples
A real Lie group is a group which is also a finite-dimensional real smooth manifold, and in which the group operations of multiplication and inversion are smooth maps. Smoothness of the group multiplication
means that μ is a smooth mapping of the product manifold G×G into G. These two requirements can be combined to the single requirement that the mapping
be a smooth mapping of the product manifold into G.
Read more about this topic: Lie Group
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