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Results tagged with lie-groups
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user 7311
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
56
votes
What is the situation with Hilbert's Fifth Problem?
The OP says:
" ...Recently, Palais wrote about it in the Notices but he only treats the old story from the 1950s and seems not to be aware of Olver’s facts."
Actually, I am aware of Olver's work and …
- 15.3k
23
votes
Accepted
Monotone functions are differentiable a.e. and Hilbert's Fifth Problem: what's the connection?
Well, I cannot say for certain, but I did know Gleason well (he was my thesis advisor, and we wrote a paper together after that) and I have written an essay about Gleason's work on the Fifth Problem ( …
- 15.3k
17
votes
1
answer
500
views
Is a smooth action of a semi-simple Lie group linearizable near a stationary point?
Suppose that $G$ is a semi-simple Lie group that acts smoothly (i.e., $C^\infty$) on a smooth, finite dimensional manifold $M$. Does it follow that the action of $G$ is linearizable near any stationar …
- 15.3k
8
votes
Accepted
Lie group action with no slice
Recall that if a free action of G on M has a slice S at a point x then the natural map of G x S into M given by (g,s) maps to gs would be a diffeomorphism onto a tubular neighborhood of the orbit Gx. …
- 15.3k
6
votes
Action of the group of isometries on a manifold
It is easy to see that any metrically homogeneous, locally compact, metric space, $X$, is complete. If $p$ is some point of $X$ then, by local compactness, for some $\epsilon > 0$, the closed $\epsilo …
- 15.3k
4
votes
Does a finite-dimensional Lie algebra always exponentiate into a universal covering group
The short answer to 3. is "no". The simplest example is the circle group, $e^{it}$ of complex numbers of absolute value 1, (thought of as a $1 \times 1$ matrices), its Lie algebra $A$ consists of the …
- 15.3k
3
votes
What are the invariant Pseudo-differential operators on a Lie group?
It seems to me that an interesting "first step" or sub-problem---and one that should be fairly straightforward, is to characterize the space of invariant symbols of pseudo differential operators on a …
- 15.3k
3
votes
Accepted