Timeline for Lie group flows [closed]
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 14, 2021 at 12:53 | history | closed |
Ben McKay alvarezpaiva Eric Peterson Stefan Waldmann Bugs Bunny |
Not suitable for this site | |
| Nov 28, 2021 at 12:37 | comment | added | Tom Goodwillie | @Alexander Schmeding: I mean, while it can be useful to generalize the idea of Lie group to some infinite-dimensional cases, it will not be true that all the theorems of Lie group theory extend. | |
| Nov 27, 2021 at 8:09 | comment | added | Alexander Schmeding | @Tom Goodwillie: What do you mean by Diff$(M)$ is not really a Lie group? ITS a classical result that the diffeomorphism group is an Infinite dimensional Lie group. | |
| Nov 27, 2021 at 7:27 | review | Close votes | |||
| Dec 14, 2021 at 12:56 | |||||
| Nov 27, 2021 at 7:08 | comment | added | Ben McKay | The definition of a group action is standard; for Lie group actions, one only requires smoothness. Look in any undergraduate differential geometry textbook that covers Lie groups. | |
| Nov 27, 2021 at 4:37 | comment | added | Tom Goodwillie | I would say that what you are calling a ``$G$-flow'' is usually known as a smooth action of $G$ on $M$. Yes, there are plenty of these. Although $Diff(M)$ is not really a Lie group, it does have a Lie algebra associated with it, namely the space $\Gamma (TM)$ of smooth tangent fields. A smooth $G$-action gives a Lie algebra map to $\Gamma (TM)$, and if $G$ is connected then the Lie algebra map determines the action. | |
| Nov 27, 2021 at 1:59 | comment | added | user44191 | It's not quite precisely what you want, but I think you're looking at things along the lines of the moment map. | |
| Nov 27, 2021 at 1:51 | history | edited | LSpice | CC BY-SA 4.0 |
TeXing
|
| S Nov 27, 2021 at 1:45 | review | First questions | |||
| Nov 27, 2021 at 1:59 | |||||
| S Nov 27, 2021 at 1:45 | history | asked | Frey | CC BY-SA 4.0 |