Timeline for Universal enveloping algebra and the algebra of invariant differential operators
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4, 2018 at 15:31 | answer | added | dhy | timeline score: 6 | |
| Apr 4, 2018 at 13:53 | comment | added | truebaran | Thank you for your comment: could you please provide some more details (maybe as an answer)? | |
| Apr 3, 2018 at 18:05 | comment | added | dhy | Here is one way to see this: There is a map from the universal enveloping algebra to the algebra of differential operators landing in right-invariant operators. Your question seems to be why this map is an isomorphism; for this, it suffices to check this statement after taking associated gradeds w/r/t the PBW&order filtrations. The associated graded of $\mathcal{D}_G$ is isomorphic to $\mathcal{O}_G\otimes\operatorname{Sym}^{\bullet}\mathfrak{g},$ with $G$ acting purely on the first factor. | |
| Apr 3, 2018 at 14:53 | history | asked | truebaran | CC BY-SA 3.0 |