  For $\mathfrak{g}$ a simple Lie algebra and $G$ its adjoint group, the
Chevalley map and work of Coxeter gives a concrete description of the algebra
of $G$-invariant polynomials on $\mathfrak{g}$ in terms of traces over various
representations. Here we provide an extension of this description to
$G$-invariant tensors on $\mathfrak{g}$, although restricted to only providing
generators and only for the classical Lie algebras.
