Timeline for Closed subgroups of $\mathrm{SO}(4)$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 3, 2023 at 21:55 | comment | added | zeta | Note that Spin(4) = SU(2) x SU(2). Can you answer: Does SO(4)=Spin(4)/Z_2 contain a subgroup SU(2) precisely? ( thanks!) | |
| May 27, 2016 at 16:08 | comment | added | Sean Lawton | @FriedrichKnop Thank you for the helpful comment! | |
| May 27, 2016 at 15:28 | comment | added | Friedrich Knop | References to the classification of finite subgroups can be found in mathoverflow.net/questions/37136/…. | |
| May 26, 2016 at 23:00 | comment | added | Igor Khavkine | I don't know if the OP intended to leave this door open, but discrete subgroups are also closed and those can't be classified just by looking at the Lie algebra (AFAIK). | |
| May 26, 2016 at 22:11 | comment | added | YCor | Yes, although Goursat's lemma reduces to a careful description of all quotients of all finite subgroups. Also it does not reduce to Goursat's lemma in all case, because in principle you could find closed subgroup with some non-closed projection (actually in the precise case of $SU(2)\times SU(2)$ are aren't, but there would be in $SU(3)\times SU(3)$.) | |
| May 26, 2016 at 21:49 | comment | added | Sean Lawton | I added some further detail and clarification. | |
| May 26, 2016 at 21:48 | history | edited | Sean Lawton | CC BY-SA 3.0 |
added 61 characters in body
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| May 26, 2016 at 21:27 | comment | added | YCor | "this gives the closed subgroups of $SU(2)$ and hence of $SU(2)\times SU(2)$": this is not correct. Understanding the closed subgroups of $G$ and $H$ is just a first step before a description of subgroups of $G\times H$. "More generally, all simple subgroups" is also weird: the question is not just about simple subgroups. | |
| May 26, 2016 at 20:33 | history | answered | Sean Lawton | CC BY-SA 3.0 |