  We discuss locally simply transitive affine actions of Lie groups G on
finite-dimensional vector spaces such that the commutator subgroup [G,G] is
acting by translations. In other words, we consider left-symmetric algebras
satisfying the identity [x,y].z=0. We derive some basic characterizations of
such left-symmetric algebras and we highlight their relationships with the
so-called Novikov algebras and derivation algebras.
