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
Famous quotes containing the words lie and/or groups:
“It is all right for the lion and the lamb to lie down together if they are both asleep, but if one of them begins to get active it is dangerous.”
—Crystal Eastman (1881–1928)
“And seniors grow tomorrow
From the juniors today,
And even swimming groups can fade,
Games mistresses turn grey.”
—Philip Larkin (1922–1986)