Timeline for Coordinate-free description of an alternating trilinear form on pure octonions
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2020 at 10:38 | comment | added | Mikhail Borovoi | My calculation using Table 5 in the book by Onishchik and Vinberg shows that $V\otimes S^2 V$ does not contain the trivial representation. Thus indeed there is nonzero invariant symmetric bilinear form. | |
| Nov 30, 2020 at 22:27 | comment | added | YCor | Also if I'm correct, the 3rd symmetric power, of dimension 84, decomposes in irreducibles as 77+7. In particular it doesn't contain the trivial representation, so there's no nonzero invariant symmetric trilinear form. (While the 3rd alternating power, of dimension 35, decomposes as 27+7+1.) | |
| Nov 30, 2020 at 16:43 | comment | added | Mikhail Borovoi | Excellent! Thank you! | |
| Nov 30, 2020 at 16:41 | vote | accept | Mikhail Borovoi | ||
| Nov 30, 2020 at 16:37 | comment | added | YCor | I did a little brute Sage program this time to check all cases (to check the vanishing on all 343 possible triples). | |
| Nov 30, 2020 at 16:17 | comment | added | Mikhail Borovoi | How did you check that the symmetrized form vanishes? | |
| Nov 30, 2020 at 16:03 | history | answered | YCor | CC BY-SA 4.0 |