"... Lie algebras have a significance reaching beyond the domain of algebra, because they play such an important role in the theory of Lie groups. Thus, classical Lie algebra theory is strongly dominated by the fact that the finite-dimensional analytic representations of a simply connected analytic group are identifiable with the finite-dimensional representations of its Lie algebra. In the theory of infinite-dimensional representations, the connection with Lie algebra representations is somewhat tenuous, but it is nevertheless at the core of the major advances made in that theory during the last 30 years."