Timeline for Poisson ideals vs. ideals generated by Poisson central elements
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 29, 2014 at 15:57 | vote | accept | Allen Knutson | ||
| Jul 29, 2014 at 14:29 | comment | added | Brent Pym | Nicola's answer below certainly gives the desired counterexample. I just wanted to mention that if $I$ is already radical then there is a simple obstruction to equality of $I$ and $\langle I\cap Z \rangle$. Namely, the Poisson bracket descends to a Lie algebra structure on $I/I^2$ (the "co-normal Lie algebra"). If $I$ is generated by elements of $Z$ then this Lie bracket will be abelian, but most conormal algebras are not. For example, for the maximal ideal $\mathfrak{m}$ defining the origin in the dual of a Lie algebra $\mathfrak{g}$, we have $\mathfrak{m}/\mathfrak{m}^2\cong\mathfrak{g}$ | |
| Jul 29, 2014 at 7:55 | answer | added | Nicola Ciccoli | timeline score: 5 | |
| Jul 29, 2014 at 6:38 | answer | added | Peter Michor | timeline score: 0 | |
| Jul 29, 2014 at 0:17 | history | asked | Allen Knutson | CC BY-SA 3.0 |