Timeline for Lifting matrices mod 2 to integers.
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2010 at 18:27 | comment | added | Petya | Nice argument, Robin! | |
| Mar 15, 2010 at 18:12 | comment | added | Robin Chapman | This is a bit weaker than Petya's original question since there the entries in the lifted matrix are constrained to be 0, 1 or -1. For the proof of the surjectivity of $SL_n(\mathbf{Z})\to SL_n(\mathbf{Z}/N\mathbf{Z})$ my favoured argument goes roughly as follows. Show that $SL_n(\mathbf{Z}/N\mathbf{Z})$ is generated by elementary matrices of the form $I + E_{ij}$ where $E_{ij}$ is a matrix unit with $i\ne j$. As these matrices all lie in the image, the map is surjective. I haven't seen this argument in the textbooks :-) | |
| Mar 15, 2010 at 16:29 | comment | added | HenrikRüping | ahh I see. should read the questions more carefully . . . | |
| Mar 15, 2010 at 16:24 | comment | added | Petya | Thank you. See my remark to the original question -- it seems you are proving it. I note that Richard's proof also works for it. | |
| Mar 15, 2010 at 15:36 | history | answered | HenrikRüping | CC BY-SA 2.5 |