Could anybody give an example of maximal ideal $M$ of a Lie algebra $L$ such that $\dim \frac{L}{M}>1$?
Actually, I'd like to know at least one example of semiprime Lie algebra, but it is not semisimple. I read several theorems about semiprime Lie algebras but no author has exhibited an example of such algebra to make sure the object of study exists.
Can anyone help me with this? Any suggestions are appreciated.
Definition: A Lie algebra $L$ is said to be semiprime if for every nonzero ideals $I$, $[I,I]\neq 0$.