For all results obtained,
attention is restricted to algebraically closed fields of characteristic zero. An affine
algebraic group is said to have property (∗) if the intersection of its center and its
radical is unipotent. Given a Lie algebra L, a characterization is obtained of those
affine algebraic groups G having property (∗) for which an injection L →ℒ(G) exists
whose image is algebraically dense. This is applied to obtain a result concerning the
embedding of Lie algebras into algebraic Lie algebras, and to questions about the
Hopf algebra of representative functions of a Lie algebra L in the case where L is
algebraic.
