  In this paper, we construct a faithful representation with the lowest
dimension for every complex Lie algebra in dimension $\leq 4$. In particular,
in our construction, in the case that the faithful representation has the same
dimension of the Lie algebra, it can induce an \'etale affine representation
with base zero which has a natural and simple form and gives a compatible
left-symmetric algebra on the Lie algebra. Such affine representations do not
contain any nontrivial one-parameter subgroups of translation.
