Timeline for Transitivity of $Spin(7)$ in triples of vectors
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 17, 2016 at 5:27 | vote | accept | Jjm | ||
| Apr 16, 2016 at 18:41 | comment | added | asv | @BenMcKay : you are right. The dimension is 21. Sorry for the mistake. | |
| Apr 16, 2016 at 18:34 | comment | added | Ben McKay | In fact $\operatorname{Spin}(7)$ acts on the orthogonal quadruples preserving the Cayley 4-planes. | |
| Apr 16, 2016 at 18:31 | comment | added | Sebastian Goette | Yes of course, and the stabiliser of $SU(3)$ acting on $S^5$ is $SU(2)$, which has dimension $3$. In particular, Spin(7) does not act transitively on quadruples. | |
| Apr 16, 2016 at 18:28 | comment | added | Ben McKay | But I think that $\operatorname{Spin}(7)$ has dimension 21. | |
| Apr 16, 2016 at 18:26 | history | answered | Ben McKay | CC BY-SA 3.0 |