Timeline for Ergodic action on product spaces
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 16, 2021 at 8:31 | comment | added | Uri Bader | If $G$ is contained in a semisimple Lie group $H$ and the action on one of the spaces, say $X_1$ extends to $H$ then the $G$-action on $X$ will be ergodic. This is because the $H$-action on $X_1$ will be mixing, hence also the $G$-action. | |
| Sep 15, 2021 at 21:19 | comment | added | Osheaga | Thank you, I will look it up and see if if it's helpful. The Group $G$ is subgoup of a a semisimple Lie group. | |
| Sep 6, 2021 at 12:48 | comment | added | Uri Bader | You mention Baily-Borel compactification, so I suppose your group $G$ is more then just a locally compact group. Is it a semisimple Lie group? Are you aware of Howe-Moore theorem? | |
| Sep 5, 2021 at 7:41 | comment | added | Pietro Majer | If e.g. $X_1$ and $X_2$ are copies of $G:=\mathbb R/Z$ with the standard structure, isn't any set $\{(x,y):x-y\in A\}$ invariant, for any fixed $A\subset\mathbb G$? What am I missing? | |
| Sep 4, 2021 at 21:18 | history | asked | Osheaga | CC BY-SA 4.0 |