Timeline for Poisson ideals vs. ideals generated by Poisson central elements
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 9, 2018 at 13:09 | comment | added | Alex M. | @NicolaCiccoli: Yes, this explicit notation makes things clear. | |
| Apr 9, 2018 at 6:23 | comment | added | Nicola Ciccoli | @Alex M. Yes they are the coordinate functions and no I do not see any problem with antisymmetry. It is the Poisson bracket given by the (evidently) antisymmetric bivector $\pi=xy\partial_x\wedge\partial_y$. Is this clearer? | |
| Apr 8, 2018 at 15:10 | comment | added | Alex M. | @NicolaCiccoli: I apologize for the intrusion, but do $x$ and $y$ represent the coordinate functions on $\mathbb R^2$? If so, your Poisson bracket is not antisymmetric, so I'm obviously misinterpreting your notations. | |
| Jul 30, 2014 at 8:25 | comment | added | Nicola Ciccoli | You also asked for references, I guess that here mathnet.or.kr/mathnet/paper_file/glasgow/Gordon/poisord.pdf you may find some pieces fo the general theory... | |
| Jul 30, 2014 at 6:37 | comment | added | Nicola Ciccoli | Maybe more than an analogue; what is around here is the infinitesimal action of all the Hamiltonian vector fields... | |
| Jul 29, 2014 at 18:51 | comment | added | Allen Knutson | Okay, so the group-action analogue is that a $G$-invariant subvariety may fail to be the intersection of a number of $G$-invariant hypersurfaces. | |
| Jul 29, 2014 at 15:57 | vote | accept | Allen Knutson | ||
| Jul 29, 2014 at 10:38 | comment | added | Nicola Ciccoli | To put it another way: being a symplectic leaf is still quite far from being a level set of Casimir functions. There are many examples of algebraic Poisson manifolds with dense leaves, or leaves which are dense inside closed submanifolds. | |
| Jul 29, 2014 at 8:27 | comment | added | Stefan Waldmann | Being a Poisson ideal, $I$ is also a associative ideal. So to make things interesting, it should not contain the constants. I think your example completely settles the question (in the negative). | |
| Jul 29, 2014 at 8:10 | history | edited | Nicola Ciccoli | CC BY-SA 3.0 |
added 196 characters in body
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| Jul 29, 2014 at 7:55 | history | answered | Nicola Ciccoli | CC BY-SA 3.0 |