Timeline for Almost but not quite a Lie algebroid: what is it?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 19, 2015 at 4:26 | vote | accept | José Figueroa-O'Farrill | ||
| Jul 19, 2015 at 0:41 | comment | added | Daniele Sepe | With pleasure, @JoséFigueroa-O'Farrill! I have included an answer to the question below, but I am sure that you have already worked it out :) | |
| Jul 19, 2015 at 0:39 | answer | added | Daniele Sepe | timeline score: 9 | |
| Jul 19, 2015 at 0:10 | comment | added | José Figueroa-O'Farrill | Thank you, @Daniele! I didn't know this paper and it is very useful. | |
| Jul 18, 2015 at 23:02 | comment | added | José Figueroa-O'Farrill | @DanieleSepe: Hi! Indeed, I have a Jacobi structure on a nontrivial line bundle, but I thought that I had more that that, since I have also the map from sections to vector fields, which is why I thought at first that I would have a Lie algebroid. | |
| Jul 18, 2015 at 22:16 | comment | added | Daniele Sepe | Hi José, another possibly silly question: is your bracket local? That is, does $supp [e_1,e_2] \subset supp \, e_1 \cap supp \, e_2$ hold, where $supp$ denotes the support and $e_1,e_2 \in \Gamma(E)$ are (possibly locally defined) sections? I suspect that the answer to the above question is yes; in which case, you are in the presence of a Jacobi structure (I can write a longer answer with some references if that is the case). | |
| Jul 18, 2015 at 15:22 | history | edited | José Figueroa-O'Farrill | CC BY-SA 3.0 |
added some additional information to illustrate that this is far from generic.
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| Jul 17, 2015 at 3:55 | comment | added | José Figueroa-O'Farrill | Not a silly question and perhaps I should have mentioned it. I find that $$\rho(f e)(g) - f \rho(e)(g) = T_e(df,dg),$$ where $T_e$ is a bivector. | |
| Jul 17, 2015 at 3:21 | comment | added | David Roberts♦ | Silly question: How far from being $C^\infty(M)$-linear is $\rho$? | |
| Jul 17, 2015 at 2:53 | history | asked | José Figueroa-O'Farrill | CC BY-SA 3.0 |