Timeline for Connectedness of Centralizers in $GL_n$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 17, 2011 at 18:52 | comment | added | darij grinberg | Thanks to Brian Conrad for explaining me why the procedure I proposed in the comment above doesn't work. The closure of the set of powers of $g$ needs not be a torus. | |
| May 16, 2011 at 15:47 | answer | added | Jim Humphreys | timeline score: 14 | |
| May 16, 2011 at 15:09 | comment | added | darij grinberg | Milne, ALA ( jmilne.org/math/CourseNotes/ala.html ), I, Exercise 18-1: "Use the criterion (18.1) to show that the centralizer of a torus in a connected algebraic group is connected." Now the question is whether you can find, for your element $g$ or $s$, a torus which has the same centralizer as the element. Probably something like the closure of the set of powers of $g$ (rsp. $s$)? | |
| May 16, 2011 at 13:54 | answer | added | Neil Strickland | timeline score: 4 | |
| May 16, 2011 at 13:14 | history | asked | HNuer | CC BY-SA 3.0 |