Timeline for Info on Symplectic/Orthogonal groups of Gl(n,R); R a ring, not necessarily division ring.
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 26, 2015 at 11:32 | answer | added | Anupam Singh | timeline score: 1 | |
| Jul 7, 2011 at 2:41 | answer | added | Larry | timeline score: 1 | |
| Jun 21, 2011 at 8:09 | comment | added | Tom De Medts | In addition to Andy Putnam's comment, you might want to have a look at the related question mathoverflow.net/questions/59884/… that I asked some time ago. | |
| Jun 21, 2011 at 6:39 | answer | added | mathphysicist | timeline score: 2 | |
| Jun 21, 2011 at 5:47 | comment | added | Andy Putman | To give you an idea of how hard it is to do linear algebra over rings that aren't fields, let's forget symplectic/orthogonal groups for a second and consider $G_n = SL_n(\mathbb{Z}[t,t^{-1}])$. In an absolute tour de force, Suslin proved that $G_n$ is generated by elementary matrices for $n$ at least $3$ (and, in particular, is finitely generated). However, for $n=2$ it is not known whether or not $G_n$ is generated by elementary matrices or finitely generated, though a deep theorem of Krstic-McCool shows that it is not finitely presentable. | |
| Jun 21, 2011 at 4:59 | comment | added | Andy B | Are these linear algebraic groups defined over Z? If so you can consider them as group schemes over any ring. | |
| Jun 21, 2011 at 2:33 | comment | added | Andy Putman | Is there something specific you want to know? It is a rather big subject, and it is hard to say anything nontrivial about totally general rings... | |
| Jun 21, 2011 at 2:07 | history | asked | Larry | CC BY-SA 3.0 |