Definition 5

Let $g$ be a Lie algebra and $h$ a Lie subalgebra of $g$. $h$ is called reductive in $g$ if the representation $x \mapsto \operatorname{ad}_g x$ of $h$ is semi-simple.

This representation admits as subrepresentation the adjoint representation of $h$. Hence, if $h$ is reductive in $g$, $h$ is reductive. On the other hand, to say that a Lie algebra is reductive in itself is equivalent to saying that it is reductive.