Timeline for When is the image of the adjoint representation of a real algebraic group Zariski closed?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 8, 2015 at 9:24 | vote | accept | Mathemagician | ||
| Oct 7, 2015 at 20:21 | answer | added | Mikhail Borovoi | timeline score: 3 | |
| Oct 7, 2015 at 18:31 | comment | added | Mikhail Borovoi | I think that compactness of $G(\mathbb{R})$ is a sufficient condition for the image of the adjoint representation of a real algebraic group to be Zariski closed. Indeed, then the image is compact, hence Zariski closed, see Onishchik and Vinberg, Lie Groups and Algebraic Groups, Section 3.4.4, Theorem 5. | |
| Oct 7, 2015 at 18:16 | comment | added | Mikhail Borovoi | No, at least for $n=2$. The image will be the identity component of the group of $\mathbb{R}$-points of a group isomorphic to $\mathrm{SO}(2,1)$, hence not Zariski closed. | |
| Oct 7, 2015 at 17:43 | history | asked | Mathemagician | CC BY-SA 3.0 |