Quotient Group - Quotients of Lie Groups

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.