Timeline for Automorphisms of $GL_n(\mathbb{Z})$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 9, 2019 at 1:42 | vote | accept | cheyne | ||
| Jan 7, 2019 at 2:24 | vote | accept | cheyne | ||
| Jan 9, 2019 at 1:42 | |||||
| Jan 6, 2019 at 23:23 | answer | added | KConrad | timeline score: 15 | |
| Jan 6, 2019 at 18:45 | comment | added | cheyne | I completely understand. Thanks again! | |
| Jan 6, 2019 at 18:26 | comment | added | YCor | I'm lazy at the moment to fill in the details, this is why a comment is maybe better to start with. | |
| Jan 6, 2019 at 18:24 | comment | added | cheyne | @YCor Thank you! My first sentence was just a motivation in case it was helpful. Would you like to rewrite this as an answer so I can select it? It would be helpful if you added a reference or added a few more details about the semi-direct product with tau. | |
| Jan 6, 2019 at 17:31 | comment | added | YCor | I'm not sure of the meaning of your first sentence, but for the second one, the automorphism group for $n\ge 3$ is reduced to the "obvious" one, namely $\mathrm{PGL}_n(\mathbf{Z})\rtimes\{\tau\}$ where $\tau$ is the inverse-transpose involutive automorphism. (Essentially, Mostow rigidity reduces to compute the normalizer in the real automorphism group, i.e., to show that $\mathrm{SL}_n(\mathbf{Z})$ equals its own normalizer in $\mathrm{SL}_n(\mathbf{R})$.) However it's very plausible that this was known earlier in this case by a direct algebraic approach. | |
| Jan 6, 2019 at 17:07 | history | asked | cheyne | CC BY-SA 4.0 |