"A Lie algebra is said to be algebraic if it is isomorphic with the Lie algebra of an affine algebraic group. In view of the fact that entirely unrelated affine algebraic groups (typically, vector groups and toroidal groups) may have isomorphic Lie algebras, this notion of algebraic Lie algebra calls for some clarification. The most relevant result in this direction is due to M. Goto. It says that a finite- dimensional Lie algebra L over a field of characteristic 0 is algebraic if and only if the image of L under the adjoint representation is the Lie algebra of an algebraic subgroup of the group of automorphisms of L ..."