Derived algebra
= Derived algebra
{title2=$\mathcal D(\mathfrak g)=[\mathfrak g,\mathfrak g]$}
The derived algebra is the linear span of all <Lie brackets> $[x,y]$ in a <Lie algebra>. The <Jacobi identity> makes it an <ideal of a Lie algebra>. Its quotient is the largest <Abelian Lie algebra> quotient of $\mathfrak g$.