Timeline for In a compact lie group, can two closed connected subgroups generate a non-closed subgroup?
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S yesterday | vote | accept | Bob Yuncken | ||
| Apr 22, 2011 at 6:58 | comment | added | Bob Yuncken | Yes, it is true that $L$ can be written in this form, but that's a consequence of the solution to the problem. I can't see how to argue that directly. | |
| Apr 21, 2011 at 12:23 | comment | added | Mikhail Borovoi | @George: It is true that $L$ can be written in this form, see my answer... | |
| Apr 21, 2011 at 10:06 | comment | added | George Lowther | The result would follow easily if every element of $L$ could be written as $g_1g_2\ldots g_N$ for $g_i\in H\cup K$ and a fixed $N$. In that case, $L$ would be a continuous image of the compact space $(H\cup K)^N$, hence compact. I'm not sure if $L$ can always be written in this form, but it seems reasonable. | |
| Apr 21, 2011 at 8:04 | vote | accept | Bob Yuncken | ||
| S yesterday | |||||
| S Apr 21, 2011 at 8:04 | vote | accept | Bob Yuncken | ||
| Apr 21, 2011 at 8:04 | |||||
| Apr 21, 2011 at 8:04 | vote | accept | Bob Yuncken | ||
| S Apr 21, 2011 at 8:04 | |||||
| S Apr 21, 2011 at 8:04 | vote | accept | Bob Yuncken | ||
| Apr 21, 2011 at 8:04 | |||||
| Apr 21, 2011 at 8:04 | vote | accept | Bob Yuncken | ||
| S Apr 21, 2011 at 8:04 | |||||
| S Apr 21, 2011 at 3:45 | vote | accept | Bob Yuncken | ||
| Apr 21, 2011 at 3:46 | |||||
| S Apr 21, 2011 at 3:45 | vote | accept | Bob Yuncken | ||
| S Apr 21, 2011 at 3:45 | |||||
| Apr 21, 2011 at 3:45 | vote | accept | Bob Yuncken | ||
| S Apr 21, 2011 at 3:45 | |||||
| Apr 21, 2011 at 3:45 | vote | accept | Bob Yuncken | ||
| Apr 21, 2011 at 3:45 | |||||
| Apr 20, 2011 at 23:13 | answer | added | Jim Humphreys | timeline score: 12 | |
| Apr 20, 2011 at 22:17 | answer | added | Mikhail Borovoi | timeline score: 16 | |
| Apr 20, 2011 at 20:50 | comment | added | Ian Agol | I believe that the subgroup will be closed, given by the exponential of the subalgebra of the Lie algebra of G generated by the two subalgebras of H and K. The kind of argument I have in mind is similar to the proof of Theorem 0.4 in these notes: math.berkeley.edu/%7Eianagol/261A.F09/Simplegroups.pdf | |
| Apr 20, 2011 at 20:36 | comment | added | Somnath Basu | I took the liberty to add the tag of "Lie groups". | |
| Apr 20, 2011 at 20:35 | history | edited | Somnath Basu |
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| Apr 20, 2011 at 20:11 | history | asked | Bob Yuncken | CC BY-SA 3.0 |