Timeline for What is the cubic Casimir element of $\mathfrak{sl}_3$?
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8 events
| when toggle format | what | by | license | comment | |
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| Oct 25, 2023 at 11:30 | history | edited | Martin Sleziak |
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| Oct 25, 2023 at 11:28 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tag
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| Oct 25, 2023 at 11:22 | answer | added | Marco Farinati | timeline score: 0 | |
| Nov 28, 2014 at 9:12 | comment | added | Qiaochu Yuan | en.wikipedia.org/wiki/Harish-Chandra_isomorphism | |
| Nov 28, 2014 at 9:07 | answer | added | M T | timeline score: 7 | |
| Nov 28, 2014 at 5:56 | comment | added | Venkataramana | you may want to look at the book by Humphreys on Lie algebras. The explicit isomorphism between the associated graded of the enveloping algebra of a semi-simple Lie algebra $\mathfrak g$ and the symmetric algebra of $\mathfrak g$ is given there from which you can deduce that the space of invariants of the enveloping algebra (i.e. its centre) is isomorphic to the space of $\mathfrak g$ invariants in the symmetric algebra; the latter is a polynimial algebra with some well chosen generators. In your case, there is one in degree three, namely the determinant of a traceless $3\times 3$ matrix. | |
| Nov 28, 2014 at 4:35 | review | First posts | |||
| Nov 28, 2014 at 4:42 | |||||
| Nov 28, 2014 at 4:35 | history | asked | mokim | CC BY-SA 3.0 |