Quotients of Lie Groups
If G is a Lie group and N is a normal Lie subgroup of G, the quotient G / N is also a Lie group. In this case, the original group G has the structure of a fiber bundle (specifically, a principal N-bundle), with base space G / N and fiber N.
For a non-normal Lie subgroup N, the space G / N of left cosets is not a group, but simply a differentiable manifold on which G acts. The result is known as a homogeneous space.
Read more about this topic: Quotient Group
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