Abstract
For
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
g
in terms of traces over various representations. Here we provide an extension of this description to
G
-invariant tensors on
g
, although restricted to only providing generators and only for the classical Lie algebras.