Timeline for Cartesian square root of a measure preserving action
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 15, 2016 at 16:36 | comment | added | Vladimir | Ideally some kind of characterization would be good, or at least an interesting sufficient condition. But anything interesting would be interesting! And at this point would suffice for being an acceptable answer. | |
| Apr 15, 2016 at 12:00 | comment | added | Uri Bader | Could you please try to specify what do you mean by "when"? What kind of answer do you expect? | |
| S Dec 4, 2015 at 8:39 | history | bounty ended | CommunityBot | ||
| S Dec 4, 2015 at 8:39 | history | notice removed | CommunityBot | ||
| Nov 30, 2015 at 0:32 | history | edited | Vladimir | CC BY-SA 3.0 |
Changed title slightly, according to comment by user
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| Nov 26, 2015 at 14:51 | comment | added | Lee Mosher | Perhaps "Cartesian square root" would be a better terminology. | |
| S Nov 26, 2015 at 7:03 | history | bounty started | Vladimir | ||
| S Nov 26, 2015 at 7:03 | history | notice added | Vladimir | Draw attention | |
| Nov 24, 2015 at 15:15 | comment | added | Vladimir | Thanks again Anthony. And yes - my choice of title is a little confusing. | |
| Nov 24, 2015 at 9:10 | comment | added | Anthony Quas | The terminology "square root" is slightly difficult because Ornstein used it to mean (for $\mathbb Z$ actions) a transformation $S$ such that $S^2=T$. For i.i.d., this seems straightforward as you say (just using entropy) | |
| Nov 24, 2015 at 8:04 | comment | added | Vladimir | Thanks! For amenable groups (at least) it seems like it should be possible to take the square root of i.i.d. actions. I wonder if more can be said. | |
| Nov 24, 2015 at 6:16 | comment | added | Anthony Quas | If the $X$ action is ergodic, then the $Y$ action must be weak-mixing and hence the $X$ action must be weak-mixing. (That is you cannot find a square root like this if the $X$ action is ergodic but not weak-mixing). | |
| Nov 24, 2015 at 5:52 | history | asked | Vladimir | CC BY-SA 3.0 |