Since the center of a Lie algebra\\ mathfrak g is an abelian ideal, if\\ mathfrak g is semisimple, then its center is zero; in other words, the adjoint representation\\ operatorname is injective.
Since the center of a Lie algebra\\ mathfrak g is an abelian ideal, if\\ mathfrak g is semisimple, then its center is zero. In other words, the adjoint representation\\ operatorname is injective.