Timeline for Lie algebra with cyclic structure constants
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 16, 2016 at 22:17 | vote | accept | Hauke Reddmann | ||
| Oct 15, 2016 at 13:47 | comment | added | Victor Protsak | @Venky: Yes, with the additional assumptions you stated. | |
| Oct 15, 2016 at 13:46 | comment | added | Victor Protsak | @YCor: Thank you, as a matter of fact, I was hoping the question could be reopened. Note that extra work is needed if the field is not algebraically closed or has char 2 (there exist even nondegenerate symmetric bilinear forms). | |
| Oct 15, 2016 at 13:41 | answer | added | Victor Protsak | timeline score: 5 | |
| Oct 15, 2016 at 9:06 | comment | added | Venkataramana | I should add that the char zero field is algebraically closed | |
| Oct 15, 2016 at 8:35 | comment | added | Venkataramana | @Protsak: does it mean that every semi-simple Lie algebra over char zero field has cyclic structure constants? (Because the Killing form is symmetric and non-degenerate) | |
| Oct 15, 2016 at 8:00 | history | reopened |
YCor Francois Ziegler Loïc Teyssier Dan Petersen András Bátkai |
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| Oct 15, 2016 at 7:02 | comment | added | Dan Petersen | In (unnecessarily) fancy language, such a Lie algebra is an algebra over the cyclic Lie operad. | |
| Oct 15, 2016 at 5:37 | review | Reopen votes | |||
| Oct 15, 2016 at 8:00 | |||||
| Oct 15, 2016 at 5:20 | comment | added | YCor | I rewrote the question hoping that it will it be reopened so that Victor's answer can be posted. | |
| Oct 15, 2016 at 5:17 | history | edited | YCor | CC BY-SA 3.0 |
Rewrote the question which was closed as unclear
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| Oct 14, 2016 at 20:55 | comment | added | Victor Protsak | Endow your Lie algebra with the symmetric bilinear form making $\{e_i\}$ an orthornormal basis (the Gram matrix is the identity matrix). Since $c_{ij}^k=([e_i,e_j],e_k)$, what you call "cyclicity" is equivalent to the invariance of the form. | |
| Oct 14, 2016 at 19:02 | history | closed |
YCor Wolfgang Chris Godsil Stefan Kohl♦ abx |
Needs details or clarity | |
| Oct 14, 2016 at 18:25 | comment | added | Hauke Reddmann | Typo. Sorry. Corrected. | |
| Oct 14, 2016 at 18:24 | history | edited | Hauke Reddmann | CC BY-SA 3.0 |
Now where did the = come from?
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| Oct 13, 2016 at 5:25 | review | Close votes | |||
| Oct 14, 2016 at 19:05 | |||||
| Oct 12, 2016 at 20:55 | comment | added | darij grinberg | Why does $c^k_{ij} = c^i_{jk}$ define the semisimples? In $\mathfrak{sl}_2$, the bracket $\left[e,f\right]$ has a nonzero $h$-coordinate, but the bracket $\left[h,e\right]$ has no nonzero $f$-coordinate. Are you using a weirder basis? | |
| Oct 12, 2016 at 20:46 | history | asked | Hauke Reddmann | CC BY-SA 3.0 |