Timeline for Are there "reasonable" criteria for existence/non-existence of Levi factors or their conjugacy in prime characteristic?
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| Jun 24, 2022 at 21:01 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed, cf. https://meta.mathoverflow.net/q/5301/70594
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| Jul 22, 2010 at 19:53 | history | edited | Jim Humphreys | CC BY-SA 2.5 |
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| Jul 21, 2010 at 14:39 | history | edited | Jim Humphreys | CC BY-SA 2.5 |
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| Jul 21, 2010 at 13:19 | history | edited | Jim Humphreys | CC BY-SA 2.5 |
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| Jul 21, 2010 at 13:09 | vote | accept | Jim Humphreys | ||
| Apr 23, 2010 at 0:17 | history | edited | Jim Humphreys | CC BY-SA 2.5 |
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| Apr 22, 2010 at 16:00 | answer | added | George McNinch | timeline score: 3 | |
| Apr 22, 2010 at 12:36 | history | edited | Jim Humphreys | CC BY-SA 2.5 |
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| Apr 21, 2010 at 23:27 | comment | added | BCnrd | Over $k$ admitting a degree $p^2$ extension $K$ with height $\le 1$ (such as finitely generated extn of F_p with trdeg $> 1$) Ofer found likely examples of nontrivial central extension $G$ of Res_{K/k}(SL_n) by $\mathbf{G}_ a$. That Weil restriction is perfect (by hand or because SL_n is simply connected) so the central extension structure cannot split over $\overline{k}$. It would be worthwhile to see if such an example (if it really exists) may fail to have Levi over $\overline{k}$; I have not thought about it seriously. – BCnrd 11 secs ago | |
| Apr 21, 2010 at 22:56 | comment | added | Jim Humphreys | This is definitely a direction where exploration is needed, though I can't supply it. The older work on linear groups doesn't help (I only got the example in my ancient paper from Tits, who may have gotten it from Chevalley). In particular, my 1967 paper doesn't lead onward at all, though it is freely available online as other Pacific Journal papers are. Where I tried to use Lie algebras, the Frobenius kernels would be the obvious substitute to exploit for arbitrary powers of the prime. | |
| Apr 21, 2010 at 22:13 | comment | added | BCnrd | Jim, I recently went back to some of those old posts to insert warnings about lack of Levi in char > 0 (in case anyone looks at those again). Is there published reference for Chev's examples? (In Borel's alg gps book he mentions examples exist but nothing more.) Gopal and I didn't know ref, so we put discussion of G(W_2(k)) for reductive G in appendix to the p-red book. We may have chance to insert literature reference in final version, so please let me know about possible ref. asap. The next comment will address your question. | |
| Apr 21, 2010 at 21:30 | history | asked | Jim Humphreys | CC BY-SA 2.5 |