  Let $\mathfrak{g}$ be a semisimple complex Lie algebra. Recently, Lusztig
simplified the traditional construction of the corresponding Chevalley groups
(of adjoint type) using the "canonical basis" of the adjoint representation
of~$\mathfrak{g}$. Here, we present a variation of this idea which leads to a
new, and quite elementary construction of~$\mathfrak{g}$ itself from its root
system. An additional feature of this set-up is that it also gives rise to
explicit Chevalley bases of $\mathfrak{g}$.
