Timeline for $p$-adic orthogonal groups in four variables
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Dec 18, 2015 at 1:08 | vote | accept | Keivan Karai | ||
| Dec 16, 2015 at 6:15 | answer | added | Ramin | timeline score: 0 | |
| Dec 16, 2015 at 5:26 | comment | added | nfdc23 | For non-degenerate quadratic spaces $(V, q)$ and $(V', q')$ of dimension $n \ge 3$ over a field $k$, any $k$-group isomorphism ${\rm{SO}}(q) \simeq {\rm{SO}}(q')$ arises from a conformal isometry $q \simeq q'$ that is unique up to $k^{\times}$-scaling on $V$. (Indeed, Hilbert 90 reduces this to the case $k=k_s$, so then we may assume $q' = q$ and use Dieudonne's theorem (or better: the Isomorphism Theorem for split reductive groups) that the natural map ${\rm{PGO}}(q) \rightarrow {\rm{Aut}}_{{\rm{SO}}(q)/k}$ is an isomorphism.) Thus, ${\rm{SO}}(q)$ "remembers" $q$ up to conformal isometry. | |
| Dec 16, 2015 at 0:34 | history | asked | Keivan Karai | CC BY-SA 3.0 |