Timeline for Diagonalizable subgroups of a connected linear algebraic group
Current License: CC BY-SA 2.5
13 events
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| Aug 7, 2016 at 1:47 | comment | added | nfdc23 | @LSpice: Probably. Somewhat stubbornly I wanted to address arbitrary characteristic (it makes me happier), so I didn't think at all about methods specific to characteristic zero. :) | |
| Aug 5, 2016 at 12:39 | comment | added | LSpice | @nfdc23, since we're in characteristic 0 and so everything is smooth, probably @GeorgeMcNinch's comment and @JimHumphrey's answer is an easier way to think about that, no? (The reference's citation of Steinberg's connectedness theorem even in the smooth case is overkill.) | |
| Nov 2, 2015 at 15:33 | comment | added | nfdc23 | The answer for cyclic finite diagonalizable groups is affirmative for connected reductive $G$; this is Lemma 7.1 in the Appendix of arxiv.org/pdf/1210.8161.pdf (where $\mu_n$ is written, but the initial reduction to algebraically closed ground field does not use that the cyclic group is split -- i.e., constant Cartier dual -- and so it gives the result in general). | |
| Apr 8, 2011 at 13:15 | comment | added | George McNinch | For the cyclic case: If $D = \langle s \rangle$ is a cyclic diagonalizable subgroup of a connected linear algebraic group $G$, then $s$ is a semisimple element of $G$ (of finite order). In particular, $s$ and hence $D$ is contained in a maximal torus of $G$. Indeed, by [Borel LAG,11.10] $s$ is contained in a Borel subgroup of $G$, and then the claim follows from the connected solvable case [Borel LAG,10.6]. | |
| Apr 7, 2011 at 20:01 | answer | added | George McNinch | timeline score: 4 | |
| Apr 7, 2011 at 13:35 | history | edited | Mikhail Borovoi | CC BY-SA 2.5 |
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| Apr 7, 2011 at 9:17 | history | edited | Mikhail Borovoi | CC BY-SA 2.5 |
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| Apr 6, 2011 at 11:36 | history | edited | Mikhail Borovoi | CC BY-SA 2.5 |
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| Apr 6, 2011 at 11:29 | vote | accept | Mikhail Borovoi | ||
| Apr 6, 2011 at 11:25 | history | edited | Mikhail Borovoi | CC BY-SA 2.5 |
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| Apr 6, 2011 at 11:16 | answer | added | Jim Humphreys | timeline score: 9 | |
| Apr 6, 2011 at 9:53 | answer | added | Angelo | timeline score: 14 | |
| Apr 6, 2011 at 8:00 | history | asked | Mikhail Borovoi | CC BY-SA 2.5 |