  In this paper, we established the relationship among left-invariant flat
connections on Lie groups, left-symmetric algebras, Frobenius Lie algebras and
\'{e}tale prehomogeneous vector spaces, gave a one-to-one correspondence
between the left-symmetric Lie algebras with a right identity and the \'{e}tale
prehomogeneous vector spaces for a Lie group, and proved that, in essence, any
left-symmetric structure on a reductive Lie algebra has a right identity, which
implies that the classification of flat connections on a reductive Lie group
$G$ amounts to that of \'{e}tale prehomogeneous vector spaces for $G$. We
classified the \'{e}tale prehomogeneous vector spaces for $G$ with simple Levi
factors.
