= Derivation Lie algebra
{title2=$\operatorname{Der}(\mathfrak g)$}
The <derivations of a Lie algebra> form a <Lie subalgebra> of $\operatorname{End}(\mathfrak g)$ with the <commutator> bracket. The identity $[D,\operatorname{ad}x]=\operatorname{ad}(Dx)$ makes the inner derivations an <ideal of a Lie algebra>. For a complex <semisimple Lie algebra>, the <Weyl complete reducibility theorem> and the vanishing <center of a Lie algebra> imply $\operatorname{Der}(\mathfrak g)=\operatorname{ad}\mathfrak g$.
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