Timeline for Most intricate and most beautiful structures in mathematics
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 14, 2010 at 5:50 | comment | added | Sean Tilson | Thanks for the encouragement: mathoverflow.net/questions/49357/g-2-and-geometry | |
| Dec 14, 2010 at 1:57 | comment | added | Deane Yang | If Sean doesn't do this soon, I will. My vague recollection is that you look at the 7-dimensional space of imaginary octonions. Since multiplication is not associative, there is a naturally defined 3-form that expresses the non-associativity, and $G_2$ arises as the group that preserves the 3-form. The first person to try to explain the octions to me was Calabi, when I was still an undergraduate. Then Bryant explained it again, right after he showed that $G_2$ can be the holonomy group of a non-symmetric Riemannian metric. | |
| Dec 14, 2010 at 1:36 | comment | added | Spiro Karigiannis | @Sean: post it as a question, and I will be happy to give a fairly detailed answer. | |
| Dec 13, 2010 at 23:49 | comment | added | Sean Tilson | Could you elaborate on $G_2$ then? I don't know much about lie groups, but would love to hear about the geometry. | |
| Dec 13, 2010 at 18:41 | history | answered | Deane Yang | CC BY-SA 2.5 |