Timeline for Is SO(4) a subgroup of SU(3)?
Current License: CC BY-SA 4.0
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| Nov 23, 2021 at 21:06 | history | edited | Tom Goodwillie | CC BY-SA 4.0 |
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| Nov 20, 2021 at 16:17 | comment | added | YCor | However, this argument doesn't directly show that $\mathrm{SU}(2)^2$ doesn't embed into $\mathrm{SU}(3)$. | |
| Nov 20, 2021 at 16:12 | comment | added | YCor | Indeed, I had mentioned with exactly this argument that $\mathrm{SO}(5)$ doesn't embed in $\mathrm{SU}(4)$, but this applies equally to show that for no $n\ge 2$, $\mathrm{SO}(n)$ embeds into $\mathrm{SU}(n-1)$. Namely, for both $\mathrm{SO}(n)$ and $\mathrm{SU}(n)$ (and $\mathrm{SL}_n$ over any field of char$\neq 2$), for $n\ge 1$, the maximal order of a 2-elementary abelian group is $2^{n-1}$. | |
| Nov 18, 2021 at 16:03 | history | answered | Tom Goodwillie | CC BY-SA 4.0 |