Timeline for What are some interesting examples of quotients by Lie group actions?
Current License: CC BY-SA 4.0
10 events
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| Apr 25, 2023 at 10:54 | comment | added | R. Rankin | Well, there's always the catch-all: $M=Diff(M)/Diff_{x}^{1}(M)$ Where $Diff_{x}^{1}(M)$ is the group of point stabilizing diffeomorphisms on $M$. Most simple cases I'm aware of seem to be a reduction of this. | |
| Feb 16, 2022 at 1:15 | comment | added | Callum | @CarlesGelada note that "normal" wasn't required in the construction you just performed. The quotient of a Lie group by a Lie subgroup $G/H$ is a manifold with a transitive $G$-action called a homogenous space (of which there are many examples in emiliocba's answer) and indeed any manifold with transitive $G$-action is a homogeneous space with $H$ the stabiliser of a chosen point. If the subgroup is normal the manifold is also a group itself (this is effectively what "normal" is for). | |
| Feb 14, 2022 at 3:10 | history | became hot network question | |||
| Feb 13, 2022 at 21:46 | review | Close votes | |||
| Feb 15, 2022 at 4:29 | |||||
| Feb 13, 2022 at 21:42 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Feb 13, 2022 at 21:22 | history | edited | Carles Gelada | CC BY-SA 4.0 |
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| Feb 13, 2022 at 21:18 | comment | added | Carles Gelada | @NicolasTholozan I want quotients induced by a Lie group action. One of the situations these quotients occur is when you have a Lie group $G$ and a normal Lie subgroup $H$, then $H$ acts on $G$ giving a quotient manifold $G/H$ (if the action is free and proper). But I care about other group actions too, not those of Lie subgroups. | |
| Feb 13, 2022 at 20:59 | comment | added | Nicolast | I find the question a bit vague. You want quotients of what by normal subgroups of what? The quotient of a Lie group by a normal Lie subgroup is again a Lie group. Do you want examples of Lie groups having normal subgroups ? | |
| Feb 13, 2022 at 20:13 | answer | added | emiliocba | timeline score: 10 | |
| Feb 13, 2022 at 18:40 | history | asked | Carles Gelada | CC BY-SA 4.0 |