Timeline for Is every finite-dimensional Lie algebra the Lie algebra of an algebraic group?
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| Feb 21, 2017 at 6:33 | comment | added | Michaël Le Barbier | @FrancoisZiegler That's right, reading the argument today, I don't understand the comment any more. :) BTW The smallest example of a non-algebraic subalgebra is a line in a torus, if the line avoids the kernel of the exponential. In michipili.github.io/assets/math/1005.0748v1.pdf I also give more properties of the set of a algebraic subalgebras. | |
| Feb 21, 2017 at 2:26 | comment | added | Francois Ziegler | @MichaelGrünewald I think this argument does work, and answers the question. It is found in e.g. Hochschild (1981, bottom of p. 249). (Next page shows that conversely, algebraicity of $\mathrm{ad}(\mathfrak g)$ in $\mathrm{End}(\mathfrak g)$ is also sufficient for $\mathfrak g$ to be the Lie algebra of some algebraic $G$.) | |
| Oct 19, 2016 at 16:35 | comment | added | Michaël Le Barbier | This does not answer the question as a non-algebraic subalgebra of the Lie algebra of G might very well be the Lie algebra of a group – even if there is no subgroup of G whose Lie algebra is the initial one! | |
| Feb 16, 2016 at 18:15 | history | edited | Ben McKay | CC BY-SA 3.0 |
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| Oct 15, 2009 at 19:28 | history | edited | Anton Geraschenko | CC BY-SA 2.5 |
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| Oct 15, 2009 at 19:25 | vote | accept | Anton Geraschenko | ||
| Oct 15, 2009 at 6:28 | history | answered | William Slofstra | CC BY-SA 2.5 |