Timeline for $ S_4 $ subgroups and $ \operatorname{SO}_3(\mathbb{R}) $
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 28, 2022 at 4:39 | vote | accept | Ian Gershon Teixeira | ||
| Feb 24, 2022 at 4:50 | comment | added | Ian Gershon Teixeira | Ya I was thinking along the lines of intuition. And I really appreciate that! I just updated the question and I made sure to acknowledge your answer and say why I changed the question. | |
| Feb 24, 2022 at 4:24 | comment | added | LSpice | @IanGershonTeixeira, in terms of changing the question, I think the usual etiquette after an answer has been given is to ask a new question. However, no, I do not mind, as long as you clearly indicate that the question was changed after this answer was given. | |
| Feb 24, 2022 at 4:23 | comment | added | LSpice | @IanGershonTeixeira, I'm not sure I understand your argument. It is certainly possible for a connected group to intersect multiple components of a disconnected group, so I don't think your argument is yet a proof. Or were you just discussing an intuition? | |
| Feb 24, 2022 at 4:23 | comment | added | Ian Gershon Teixeira | Do you mind if I slightly change the question to perhaps make it a bit closer to what I'm really interested in? | |
| Feb 24, 2022 at 4:21 | comment | added | Ian Gershon Teixeira | ya another more geometric way to see it is that you are basically splitting up $ S_4 $ between the two connected components of an $ O_4 $ inside $ SL_5 $ ( $ A_4 $ in $ SO_4 $ and the 12 odd parity elements of $ S_4 $ in the other component of $ O_4 $). So it is not possible for any connected group to contain such a copy of $ S_4 $ since it would intersect both connected components of $ O_4 $ nontrivially contradicting connectedness. In particular $ SO_3 $ is connected so it cannot contain your $ S_4 $ subgroup. | |
| Feb 24, 2022 at 4:03 | history | undeleted | LSpice | ||
| Feb 24, 2022 at 4:00 | history | deleted | LSpice | via Vote | |
| Feb 24, 2022 at 3:59 | history | undeleted | LSpice | ||
| Feb 24, 2022 at 3:59 | history | edited | LSpice | CC BY-SA 4.0 |
Work with complex representations
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| Feb 24, 2022 at 3:17 | history | deleted | LSpice | via Vote | |
| Feb 24, 2022 at 3:17 | history | answered | LSpice | CC BY-SA 4.0 |