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 comforting when one has a sorrow to lie in the warmth of ones bed and there, abandoning all effort and all resistance, to bury even ones head under the cover, giving ones self up to it completely, moaning like branches in the autumn wind. But there is still a better bed, full of divine odors. It is our sweet, our profound, our impenetrable friendship.”
—Marcel Proust (18711922)
“In America every woman has her set of girl-friends; some are cousins, the rest are gained at school. These form a permanent committee who sit on each others affairs, who come out together, marry and divorce together, and who end as those groups of bustling, heartless well-informed club-women who govern society. Against them the Couple of Ehepaar is helpless and Man in their eyes but a biological interlude.”
—Cyril Connolly (19031974)