Timeline for How to find Casimir operators?
Current License: CC BY-SA 3.0
5 events
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| Feb 2, 2023 at 15:38 | history | edited | YCor |
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| Sep 8, 2011 at 11:28 | answer | added | H. Arponen | timeline score: 4 | |
| Aug 27, 2011 at 14:08 | comment | added | Theo Johnson-Freyd | If the Lie algebra is semisimple, then the center of its universal enveloping algebra is polynomial, and lists of good generators (often "good" means "homogeneous with respect to some grading") are known. In general, I think there is the Duflo theorem that $Z(U(\mathfrak g)) = \operatorname{Sym}(\mathfrak g)^{\mathfrak g}$ as rings, but the map is somewhat nontrivial. And anyway, this just moves the problem: certainly I don't know how, for a general Lie algebra, to compute the ring structure on $\operatorname{Sym}(\mathfrak g)^{\mathfrak g}$ (GIT quotient of adjoint action). | |
| Aug 27, 2011 at 14:02 | answer | added | Igor Rivin | timeline score: 3 | |
| Aug 27, 2011 at 11:11 | history | asked | cyl | CC BY-SA 3.0 |