Timeline for Levi decomposition in disconnected linear algebraic group (characteristic 0)?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Sep 7, 2019 at 13:49 | comment | added | YCor | It would be nice to include the statement. I expect that it says: in characteristic zero (ground field $K$), every linear algebraic $K$-group $G$ with unipotent radical $U$ has a Levi subgroup $L$, that is $G=L\ltimes U$ with $U$ unipotent. Moreover there exists a Levi factor that is defined over $K$, and all $K$-defined Levi factors $L$ are conjugate by elements of $U_K$, and $G_K=L_K\ltimes U_K$, and every $K$-defined subgroup is contained in a $K$-defined Levi factor. | |
| Jan 2, 2015 at 18:32 | comment | added | Jim Humphreys | Thanks very much for pointing out this argument in Hochschild's book (due to G.D. Mostow, who was on my thesis committee long ago). I've never studied Hochschild's treatment of structure theory systematically, since it doesn't generalize to prime characteristic. But the induction argument relying heavily on linear reductivity (including for finite groups) seems to be as elementary as possible, even though it gets fairly intricate. (Hochschild's language, like Chevalley's early one, facilitates work over arbitrary fields of characteristic 0 but then hits roadblocks.) | |
| Jan 2, 2015 at 18:23 | vote | accept | Jim Humphreys | ||
| Jan 2, 2015 at 16:36 | history | answered | m07kl | CC BY-SA 3.0 |