Timeline for Do rational points in a split reductive group act transitively on the orbits of the Cartan subalgebra (w.r.t. automorphism group of Lie algebra)?
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Mar 12, 2020 at 18:31 | comment | added | LSpice | Although you wrote that clearly, I skipped over it both in the parenthesis and in the statement of the theorem. Sorry! (Still, is it true algebraically, in characteristic 0, that automorphisms of a semisimple Lie algebra exponentiate to automorphisms of the simply connected group with that Lie algebra? I believe it, but don't know a reference.) | |
Mar 12, 2020 at 18:18 | comment | added | Mikhail Borovoi | @LSpice: In my answer ${\rm char}\,R=0$ ! | |
Mar 12, 2020 at 17:52 | comment | added | LSpice | Finally, why does $\operatorname{Aut} \mathfrak g^{\text{ss}}$ equal $\operatorname{Aut} G^{\text{sc}}$? For example, why can't there be some exotic Lie-algebra automorphisms in positive characteristic? | |
Mar 12, 2020 at 17:48 | comment | added | LSpice | The decomposition $\mathfrak g = \mathfrak z \oplus \mathfrak g^{\text{ss}}$ can fail, for example, if $R = \mathbb F_p$ and $G = \operatorname{SL}_p$. (Also the equality $\operatorname{Lie} G^{\text{sc}} = \mathfrak g^{\text{ss}}$.) | |
Mar 12, 2020 at 16:52 | history | answered | Mikhail Borovoi | CC BY-SA 4.0 |