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Results tagged with lie-groups
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user 6153
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
28
votes
Accepted
Origin of terms "flag", "flag manifold", "flag variety"?
Armand Borel's Bourbaki Seminar 121 Groupes algébriques is from 1955, and uses "drapeau" (page 7). (It's online at archive.numdam.org.) This may not be the earliest occurrence, but there is a good rea …
- 12.6k
14
votes
What is the situation with Hilbert's Fifth Problem?
http://en.wikipedia.org/wiki/Hilbert%27s_fifth_problem is a decent survey. In general in the discussion of "status" of the Hilbert problems, there are at least two recognisable routes.
Route A is the …
- 12.6k
7
votes
Why study Lie algebras?
As has been said, Lie groups are our best theory encoding continuous symmetry. Lie algebra theory, which is the infinitesimal counterpart, is a theory good enough that numerous problems can be solved …
- 12.6k
3
votes
Accepted
Is the object we get when we quotient $U(N)$ by $U(N-k)$ familar?
Putting a name to the space, it's a complex Stiefel manifold. See http://en.wikipedia.org/wiki/Stiefel_manifold. (But I wasn't the first.)
- 12.6k
1
vote
Parametrization of O(3)
If there were a really simple way we wouldn't need the concept of "gimbal lock" (http://en.wikipedia.org/wiki/Gimbal_lock). In other words the manifold in question is compact but isn't the 3-torus, an …
- 12.6k