Timeline for In dimension $n=5$, does a subgroup of $O(n)$ satisfying these properties exist?
Current License: CC BY-SA 4.0
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| Oct 21 at 13:06 | comment | added | Quoka | This may take me a while to read since I haven't done much algebra and generally work in PDEs/functional analysis. Thank you very much for the detailed answer, it looks good and I will accept it when I fully understand it. | |
| Oct 21 at 3:45 | comment | added | YCor | In the second case I omitted the case $G^\circ=\mathrm{SO}(5)$ in which Axiom 2 fails, and also I omitted the argument to deduce that $G^\circ$ is an irreducible copy of $\mathrm{SO}(3)$: since the dimension is odd, irreducibility of $G^\circ$ implies that $G^\circ$ is semisimple. For a proper subgroup of $\mathrm{SO}(5)$ this implies being locally isomorphic to $\mathrm{SO}(3)$ or $\mathrm{SO}(3)^2$ but a simple argument shows the latter cannot act faithfully irreducibly. | |
| Oct 20 at 19:39 | history | answered | YCor | CC BY-SA 4.0 |