Timeline for Are the integer matrices in SO(3,2) "boundedly generated"?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 13, 2015 at 8:36 | vote | accept | Pablo | ||
| Nov 12, 2015 at 19:10 | answer | added | Dave Witte Morris | timeline score: 6 | |
| Nov 11, 2015 at 13:06 | comment | added | Pablo | @YCor - Thanks! I have missed this point - I was thinking about $x_1^2 + x_2^2 +x_3^2 - x_4^2 - x_5 ^2$. If someone can prove the result for a slightly different bilinear form I will probably still be happy. I think that I am just looking for an example of a lattice with real rank 2, or just an example of an arithmetic group where bounded generation is conjectured to hold but has not been established yet. | |
| Nov 11, 2015 at 12:46 | comment | added | YCor | If you want to define the integral points, you have to specify more than the real type of the quadratic form, but its integral type. I guess you want something such as $x_1^2+x_2^2+x_3^2-x_4^2-x_5^2$ or $x_1x_2+x_3x_4+x_5^2$, or, better any form that is of isotropic rank 2 over the rationals (which provide infinitely many, all commensurable, possible lattices). Or possibly you also allow rational rank 1? (rational rank 0 means cocompact, in which case you don't expect bounded generation) | |
| Nov 11, 2015 at 11:53 | history | asked | Pablo | CC BY-SA 3.0 |