Timeline for Connectedness of the linear algebraic group SO_n
Current License: CC BY-SA 3.0
3 events
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| Feb 10, 2017 at 4:57 | comment | added | nfdc23 | If one treats the connectedness of Sp$_{2m}$ via an inductive fibration method in the spirit of what is done for ${\rm{SL}}_N$ then there is the modest gain that one gets the connectedness for Sp$_{2m}$ in characteristic 2 as well, which is very helpful for the inductive proof of connectedness of SO$_n$ in characteristic 2 for $n$ of both parities. | |
| Feb 10, 2017 at 2:16 | comment | added | fherzig | Incidentally, the same argument works for $Sp_{2n}$. Again one has a Cayley transform $Sp_{2n} --> Lie Sp_{2n}$ given by the same formula as for the orthogonal case. This time one uses that $Sp_2 = SL_2$ is connected. | |
| Feb 9, 2017 at 22:39 | history | answered | fherzig | CC BY-SA 3.0 |