Timeline for Why can we define the moment map in this way (i.e. why is this form exact)?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2011 at 8:27 | comment | added | Stefan Waldmann | Oh, yes. That is the one I had in mind. Sorry for not googling myself :) | |
| Feb 16, 2011 at 20:13 | comment | added | José Figueroa-O'Farrill | Thanks -- googling I just found this paper by Viktor Ginzburg: arxiv.org/abs/dg-ga/9611002. Having glanced at it very quickly, he seems to apply this to the case of Poisson Lie groups acting on a Poisson manifold and the resulting momentum mapping. | |
| Feb 16, 2011 at 14:19 | comment | added | Stefan Waldmann | Sorry, I was a little bit sloppy. Concerning the equivariant Poisson cohomology, I think I have seen something like that somewhere. Don't remember, though... :( In any case, this should be rather straightforward to cook up a reasonable Cartan like model for it. | |
| Feb 16, 2011 at 10:49 | comment | added | José Figueroa-O'Farrill | A small nitpick is that I would not say that the obstruction lies in the Poisson cohomology. This is an equivariant problem, hence the Lie algebra has to come in somewhere. The obstructions in the da Silva and Weinstein are, respectively, a Lie algebra homomorphism from $\mathfrak{g}$ to the first Poisson cohomology (which, unless I misunderstand, need not be a 1-cocycle in general) and a class in the second cohomology of $\mathfrak{g}$ with values in the zeroth Poisson cohomology. I wonder whether there is perhaps an equivariant Poisson cohomology theory where the obstruction does lie. | |
| Feb 16, 2011 at 9:19 | history | answered | Stefan Waldmann | CC BY-SA 2.5 |