Timeline for Poisson structure on the cotangent bundle
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 29, 2013 at 16:05 | vote | accept | Justin Campbell | ||
| Aug 28, 2013 at 14:34 | answer | added | Ben Webster♦ | timeline score: 3 | |
| Aug 28, 2013 at 1:38 | comment | added | AFK | The problem is that you are forgetting the last axiom in B-B's definition of a TDO, namely how $gr^1 A$ is identified with $T_X$ through $\sigma(d)(f) = fd - df$. The Poisson bracket on the cotengant bundle is the equivalent of a first ordre non commutative deformation. A simple isomorphism of algebras $gr A \simeq Sym T_X$ forgets about this information. The Poisson bracket is just a Lie bracket that is also a derivation. To get the desired result you just have to check that $\sigma$ given in degree 1 extends uniquely to the whole symetric algebra. | |
| Aug 27, 2013 at 23:18 | history | edited | Justin Campbell | CC BY-SA 3.0 |
added 472 characters in body
|
| Aug 27, 2013 at 18:10 | comment | added | Justin Campbell | Yes, I'm reading that paper. I learned about Poisson structures in a differential geometry class that emphasized computation in local coordinates, so I'm pretty bad at working with them in a nice coordinate-free way (which I very much prefer). | |
| Aug 27, 2013 at 17:35 | comment | added | AFK | Which definition of a sheaf of twisted differential operators are you working with? If you take the one from Beilinson and Bernstein, the isomorphism of Poisson structures is straightforward. | |
| Aug 27, 2013 at 16:44 | history | edited | Justin Campbell | CC BY-SA 3.0 |
edited title
|
| Aug 27, 2013 at 15:29 | history | asked | Justin Campbell | CC BY-SA 3.0 |