Timeline for Leech lattice decomposition
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 31, 2011 at 22:24 | comment | added | Paul Hjelmstad | I see you are also posting on the GAP forum. I would be interested in working with this too, since I also work with the GAP software. Could you possibly bring me up to speed with respect to the 4095 crosses in the Conway group construction, is this like the 54 crosses of Curtis's Kitten for M12 (or the related MOG construction for M24?) Thanks PGH | |
| Mar 22, 2010 at 18:13 | comment | added | Henry Cohn | Magma can compute it: AutomorphismGroup(Lattice("Lambda",24)) It will give the group to you as a subgroup of GL_24(Z), but conjugating by a basis matrix for the lattice will put it in SO(24). | |
| Mar 19, 2010 at 8:26 | vote | accept | Marek Mitros | ||
| Mar 19, 2010 at 8:11 | comment | added | Marek Mitros | Thank you for this answer ! I need some time to analyze it to create explicite decomposition. Do you know where I can find representation of Conway group Co0 as subgroup of SO(24) i.e. real 24x24 matrices ? In Atlas of finite groups there are representations over finite fields. Regards, Marek | |
| Mar 19, 2010 at 8:08 | vote | accept | Marek Mitros | ||
| Mar 19, 2010 at 8:16 | |||||
| Mar 18, 2010 at 19:26 | comment | added | Henry Cohn | I'm not sure. It'll be the centralizer of multiplication by i, so when we mod out by -1, it will be the centralizer of an involution in Co_1. There are three conjugacy classes of involutions in Co_1, but I haven't checked which one this is. The centralizers are 2^(1+8).O_8^+(2) for 2A, (2^2 x G_2(4)):2 for 2B, and 2^11:M_12:2 for 2C. | |
| Mar 18, 2010 at 17:46 | comment | added | S. Carnahan♦ | This is great! Do you by any chance know a familiar name for the subgroup of Co0 that preserves the Z[i]-module structure? | |
| Mar 18, 2010 at 16:59 | history | answered | Henry Cohn | CC BY-SA 2.5 |