Invariance of a bilinear form on a Lie algebra
= Invariance of a bilinear form on a Lie algebra
{title2=$B([x,y],z)=B(x,[y,z])$}
For a symmetric <bilinear form> on a <Lie algebra>, invariance is the displayed identity. It equivalently says that each <Adjoint representation> endomorphism is skew-adjoint with respect to $B$. The <Killing form> has this property by cyclic invariance of the <trace>.