Radical of the Killing form
= Radical of the Killing form
{title2=$\operatorname{rad}B$}
The <radical of a bilinear form> of the <Killing form> is the <ideal of a Lie algebra> $\{x:B(x,y)=0\text{ for all }y\}$. It is zero for a complex <semisimple Lie algebra>. Every element of the <center of a Lie algebra> lies in this radical.