Timeline for Left invariant metric on ${\rm SL}_n(\mathbb{R})$
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| May 8, 2017 at 16:37 | comment | added | Moishe Kohan | See my answer here for an explicit left-invariant distance function. | |
| S Mar 26, 2017 at 21:20 | history | suggested | evgeny |
not algebraic geometry
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| Mar 26, 2017 at 20:57 | review | Suggested edits | |||
| S Mar 26, 2017 at 21:20 | |||||
| S Mar 26, 2017 at 15:35 | history | suggested | Hee Kwon Lee | CC BY-SA 3.0 |
Math expression need a dollar
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| Mar 26, 2017 at 15:16 | review | Suggested edits | |||
| S Mar 26, 2017 at 15:35 | |||||
| S Aug 25, 2015 at 21:00 | history | suggested | Ali Taghavi |
I add a tag
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| Aug 25, 2015 at 20:27 | review | Suggested edits | |||
| S Aug 25, 2015 at 21:00 | |||||
| Oct 17, 2012 at 21:18 | answer | added | Robert Bryant | timeline score: 25 | |
| Sep 28, 2012 at 6:25 | answer | added | Misha | timeline score: 15 | |
| Sep 28, 2012 at 5:56 | comment | added | Misha | @Deane: Yes, of course, provided manifold is connected, otherwise one has to make some ad hoc choices for the distance between points in different components. I was just trying to point out (I guess, unsuccessfully) that not every distance is Riemannian and not every Riemannian metric defines distance. On the other hand, $SL(n,R)$ is, of course connected, so every left-invariant Riemannian metric defines a left-invariant distance function. | |
| Sep 28, 2012 at 2:34 | comment | added | Deane Yang | Mischa, it is true, however, that a Riemannian metric does define a distance function, right? So I believe your answer is a full positive answer to the question, right? | |
| Sep 27, 2012 at 22:50 | comment | added | Misha | Every Lie group has a left-invariant metric: Start with any positive definite inner product on the Lie algebra and ntranslate it to the rest of the group using left multiplication. Note also that Riemannian metric is not the same thing as a distance function. | |
| Sep 27, 2012 at 21:17 | answer | added | paul garrett | timeline score: 12 | |
| Sep 27, 2012 at 21:07 | comment | added | Anthony Quas | The discrete metric? | |
| Sep 27, 2012 at 20:09 | comment | added | safsaf32 | I mean just a distance function. | |
| Sep 27, 2012 at 19:58 | comment | added | Igor Rivin | What is an "ordinary metric"? | |
| Sep 27, 2012 at 19:27 | history | asked | safsaf32 | CC BY-SA 3.0 |