Timeline for Centralizers of regular elements are abelian
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jun 2, 2021 at 14:13 | comment | added | LSpice | Name of the particular paper: Friedman and Morgan - Automorphism sheaves, spectral covers, and the Kostant and Steinberg sections. | |
| Nov 2, 2016 at 6:19 | history | edited | Francois Ziegler |
edited tags
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| Oct 31, 2016 at 18:56 | comment | added | David Ben-Zvi | @SHP: I don't think (Lie algebra) regular centralizers (which have the same dimension as a Cartan subalgebra) are contained in Cartan subalgebras unless $X$ is itself regular semisimple (so that its centralizer is a Cartan). For example the Lie algebra centralizer of a regular nilpotent element (such as the $X$ in your post) always consists entirely of nilpotent matrices. | |
| Oct 31, 2016 at 14:17 | answer | added | Jim Humphreys | timeline score: 6 | |
| Oct 31, 2016 at 13:34 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
Removed unnecessary simple connectedness assumption
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| Oct 31, 2016 at 9:16 | vote | accept | SHP | ||
| Oct 31, 2016 at 9:15 | comment | added | SHP | @PeterMcNamara Right, thanks. The correct argument is that $Z_{\mathfrak{g}}(X)$ is contained in the generalized $0$-weight space of $\mathrm{ad}(X)$ which is a Cartan subalgebra since $X$ is regular. | |
| Oct 31, 2016 at 5:26 | answer | added | Francois Ziegler | timeline score: 6 | |
| Oct 31, 2016 at 0:03 | comment | added | Peter McNamara | A small correction: The centraliser $Z_{\mathfrak{g}}(X)$ is not always a Cartan subalgebra when X is regular (it's not self-normalising when X isn't semisimple). But for regular X, this centraliser is still abelian, so the argument that the identity component of $Z_G(X)$ is abelian still holds, without assuming simply-connectedness. | |
| Oct 30, 2016 at 17:11 | history | edited | SHP | CC BY-SA 3.0 |
added 29 characters in body
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| Oct 30, 2016 at 17:02 | answer | added | Will Sawin | timeline score: 2 | |
| Oct 30, 2016 at 17:02 | history | edited | SHP | CC BY-SA 3.0 |
added 315 characters in body
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| Oct 30, 2016 at 16:24 | history | asked | SHP | CC BY-SA 3.0 |