Timeline for Schur multiplier of a Chevalley group of type $D_5$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21 at 22:24 | vote | accept | Noah B | ||
| May 24, 2023 at 8:50 | comment | added | Dave Benson | Can I refer you to the appendix C in Conrad, "Reductive group schemes" in "Autour des schémas en groupes, I" where this is discussed in detail. In particular, a great deal of care is needed in the very definition of the special orthogonal group if $n$ is even. With the appropriate definition, it is perfect as a group scheme over Spec($\mathbb{Z})$. For the centres, see Example 1.5.2 in the same article. You might also enjoy looking at the follow-up article of Conrad, "Non-split reductive groups over $\mathbb{Z}$" in volume II of the same set. | |
| May 23, 2023 at 21:11 | comment | added | Noah B | Also, could you please provide a little bit more details about your last two deductions in the first paragraph regarding $H_2(G)$ when $G$ is of adjoint type and $H_2$ of the special orthogonal group? | |
| May 23, 2023 at 18:30 | comment | added | Noah B | Thank you for the response! That's interesting about the dependence on parity. Does that matter for the first homology? That is, do we have $EO(n,n,\mathbb{Z}) = SO(n,n,\mathbb{Z})$ for all $n\geq 5$? Or do we have to worry about parity? | |
| May 23, 2023 at 15:56 | history | answered | Dave Benson | CC BY-SA 4.0 |