Timeline for Proper compact connected subgroup of $Spin(n)$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 11, 2012 at 16:16 | answer | added | Mikhail Borovoi | timeline score: 6 | |
| Apr 11, 2012 at 15:59 | vote | accept | berl13 | ||
| Apr 11, 2012 at 15:53 | answer | added | Robert Bryant | timeline score: 8 | |
| Apr 11, 2012 at 15:20 | comment | added | berl13 | Sorry, for the confusion. I made a mistake which I edited. In fact, I am looking for the subgroup of highest dimension which satisifies these properties. | |
| Apr 11, 2012 at 15:19 | history | edited | berl13 | CC BY-SA 3.0 |
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| Apr 11, 2012 at 15:16 | comment | added | Mikhail Borovoi | Yes, it is an easier question. I assume that by $Spin(n)$ you mean the compact group $G=Spin(n)$ over $\mathbf{R}$. Then a connected subgroup of maximal rank (i.e. containing a maximal torus) of minimal dimension is a maximal torus. Its dimension is $rk(G)$, equal to $n/2$ or $(n-1)/2$ depending on whether $n$ is even or odd. The "next lowest" dimension of a connected subgroup is $rk(G)+2$. | |
| Apr 11, 2012 at 15:15 | comment | added | Robert Bryant | What's wrong with a maximal torus? That satisfies all of your conditions and is certainly the one of minimum dimension. | |
| Apr 11, 2012 at 15:02 | history | edited | Mikhail Borovoi |
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| Apr 11, 2012 at 14:07 | history | asked | berl13 | CC BY-SA 3.0 |