A reductive group is an algebraic group $G$ over an algebraically closed field such that the unipotent radical of $G$ is trivial
A reductive Lie group $G$ can be defined in terms of its Lie algebra, namely a reductive Lie group is one whose Lie algebra $\frak g$ is a reductive Lie algebra; concretely, a Lie algebra that is the sum of an abelian and a semisimple Lie algebra