Timeline for Property of a semisimple Lie algebra over complex number field
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 27, 2020 at 9:05 | comment | added | YCor | PS in my first comment I should have said "only 5 orbits modulo nonzero scalar multiplication" | |
| Feb 27, 2020 at 9:02 | comment | added | user11090426 | @YCor Thank you. | |
| Feb 27, 2020 at 5:50 | comment | added | YCor | It seems anyway that you're primarily interested in the direct implication. Yes, every element is a Lie commutator in a semisimple Lie algebra. This is already asked and answered on MathSE: math.stackexchange.com/questions/769881. | |
| Feb 27, 2020 at 5:49 | comment | added | YCor | The Lie algebra $\mathfrak{sl}_2(\mathbf{C})\ltimes\mathbf{C}^2$ is not semisimple but every element is a commutator (it has only 5 orbits under the action by automorphisms of $\mathrm{GL}_2(\mathbf{C})\ltimes\mathbf{C}^2$, so this is quite easy). | |
| Feb 27, 2020 at 5:29 | history | edited | YCor | CC BY-SA 4.0 |
formatting, English
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| Feb 27, 2020 at 4:03 | history | asked | user11090426 | CC BY-SA 4.0 |