Timeline for action of SO(q)
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 31, 2011 at 11:05 | comment | added | José Figueroa-O'Farrill | algori: you're right, of course. I've deleted my comment. | |
| May 31, 2011 at 6:18 | answer | added | Torsten Ekedahl | timeline score: 5 | |
| May 31, 2011 at 4:46 | comment | added | algori | Jose -- at first I agreed with this, but then I've realized that this map does not preserve the quadratic form $xy$. I've also just deleted an answer which purported to prove the statement by induction on the dimension of $V$. The "proof" started by saying that the statement in the case of dimension $\leq 2$ is clear, while in fact it is false in general: take the form $xy$. It has two isotropic lines. A linear map that swaps the lines has the form $(x,y)\mapsto (ay,bx)$. In order for this to preserve the form we must have $ab=1$. However, the determinant is $-ab$. | |
| May 31, 2011 at 1:20 | comment | added | algori | This is true if $\dim V$ is odd: take your map from $O(q)$ and compose with minus identity if necessary. | |
| May 30, 2011 at 23:54 | history | asked | Wanderer | CC BY-SA 3.0 |