Timeline for Why is $O(n;k)$ not connected, and has four connected components? [closed]
Current License: CC BY-SA 3.0
32 events
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| Apr 18, 2018 at 14:48 | comment | added | Venkataramana | @user123325, the intersection preserves the quadratic forms with plus and minus signs being a subgroup of $O(n,k)$ and preserves the quadratic form with only pluses being a subgroup of $O(n+k)$. Hence it preserves the sum and difference of the quadratic forms and their null spaces, Thus it preserves $R^n$ and $R^k$, hence it lies in $O(n)\times O(k)$ | |
| Apr 18, 2018 at 13:22 | comment | added | user123325 | @Venkataramana Why $O(n，k)\cap O(n+k)=O(n)\times O(k)$？ | |
| Apr 17, 2018 at 11:00 | comment | added | Venkataramana | Since $O(n,k)$ as defined is closed under transposes, the group $O(n,k)\cap O(n+k)=O(n)\times O(k)$ is a maximal compact subgroup of $O(n,k)$. Therefore, the number of connected components of $O(n,k)$ is the same as that of $O(n)\times O(k)$, and this is $2\times 2=4$. | |
| Apr 17, 2018 at 10:55 | comment | added | YCor | @j.c. thanks for flagging! I suggest to pursue the discussion on meta meta.mathoverflow.net/questions/3699/… | |
| Apr 17, 2018 at 10:54 | comment | added | YCor | @ToddTrimble what does "blocked from asking" mean? I asked this on meta as the answer (and all the discussion concerning this) can prove relevant to other MO questions: meta.mathoverflow.net/questions/3699/… | |
| Apr 17, 2018 at 10:36 | comment | added | Todd Trimble | Also the user recently posted a mathematics question at MO meta. | |
| Apr 17, 2018 at 10:35 | comment | added | Todd Trimble | Ah, here's the deal: it can't be migrated (blocked from asking). | |
| S Apr 17, 2018 at 10:33 | history | unlocked | CommunityBot | ||
| S Apr 17, 2018 at 10:33 | history | locked | CommunityBot | ||
| S Apr 17, 2018 at 10:33 | history | closed | Todd Trimble | Not suitable for this site | |
| Apr 17, 2018 at 10:33 | history | reopened | Todd Trimble | ||
| Apr 17, 2018 at 10:22 | comment | added | j.c. | I too am puzzled by this turn of events. I have flagged the question for migration by the moderators. | |
| Apr 17, 2018 at 9:52 | comment | added | YCor | Well, it has been closed by a set $A$ of 5 users, reopened by a set $B$ of 5 users (after my previous comment), and closed (instead of migrated) by a set $C$ of 5 users. While $A\cap (B\cup C)$ is empty, $B\cap C$ consists of 3 people: myself, j.c., and Francois Ziegler. Since it has not been migrated, at least 3 closing votes were not for migration, and hence it includes at least one person who voted for reopening, and certainly not me. Why such an absurd pair of votes? (when I voted for migration, one vote was cast for being "unclear"!!) | |
| S Apr 17, 2018 at 7:41 | history | unlocked | CommunityBot | ||
| S Apr 17, 2018 at 7:41 | history | locked | CommunityBot | ||
| S Apr 17, 2018 at 7:41 | history | closed |
j.c. Francois Ziegler user6976 YCor Neil Strickland |
Not suitable for this site | |
| Apr 17, 2018 at 0:48 | review | Close votes | |||
| Apr 17, 2018 at 7:41 | |||||
| Apr 17, 2018 at 0:34 | comment | added | j.c. | I voted to reopen and have now voted to migrate to math.se, per @YCor's comment. | |
| Apr 16, 2018 at 23:45 | history | reopened |
YCor j.c. Francois Ziegler Denis Serre David E Speyer |
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| Apr 16, 2018 at 22:31 | history | edited | YCor | CC BY-SA 3.0 |
added kn>0
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| Apr 16, 2018 at 13:26 | review | Reopen votes | |||
| Apr 16, 2018 at 23:46 | |||||
| Apr 16, 2018 at 13:15 | comment | added | user123325 | @YCor please paste the interlinkage. | |
| Apr 16, 2018 at 13:11 | comment | added | YCor | This was a reasonable question with an interesting and useful answer, you could have migrated it to MathSE instead of closing it. | |
| Apr 16, 2018 at 13:05 | history | closed |
Laurent Moret-Bailly Chris Godsil Bruno Martelli Andreas Blass Vladimir Dotsenko |
Not suitable for this site | |
| Apr 16, 2018 at 12:53 | comment | added | user25309 | where n and k are non-zero. If k=0, get an orthogonal group O(n) with two connected components. | |
| Apr 16, 2018 at 12:42 | answer | added | Denis Serre | timeline score: 12 | |
| Apr 16, 2018 at 12:24 | history | edited | Todd Trimble | CC BY-SA 3.0 |
improved English and tagging
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| Apr 16, 2018 at 12:20 | review | Close votes | |||
| Apr 16, 2018 at 13:06 | |||||
| Apr 16, 2018 at 11:46 | history | edited | Johannes Hahn | CC BY-SA 3.0 |
Fixed types and TeX
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| Apr 16, 2018 at 11:42 | history | edited | user123325 | CC BY-SA 3.0 |
added 13 characters in body
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| Apr 16, 2018 at 11:17 | review | First posts | |||
| Apr 16, 2018 at 12:21 | |||||
| Apr 16, 2018 at 11:12 | history | asked | user123325 | CC BY-SA 3.0 |