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Nov 1, 2014 at 15:40 comment added Kestutis Cesnavicius Thanks. I should've asked this question with $k$ algebraically closed, as I've originally intended.
Nov 1, 2014 at 14:50 comment added Laurent Moret-Bailly For a simple explicit example, you can take $k=\mathbb{R}$ and $n=1$, and take for $E$ the subgroup of $\mathrm{GL}_2$ generated by the center and the rotation $\begin{pmatrix}0&-1\\1&0\end{pmatrix}$.
Nov 1, 2014 at 14:10 history answered anon CC BY-SA 3.0