  We provide an algebraic study of the local composite operators A_\mu
A_\nu-\delta_{\mu\nu}/d A^2 and A^2, with d=4 the spacetime dimension. We prove
that these are separately renormalizable to all orders in the Landau gauge.
This corresponds to a renormalizable decomposition of the operator A_\mu A_\nu
into its trace and traceless part. We present explicit results for the relevant
renormalization group functions to three loop order, accompanied with various
tests of these results. We then develop a formalism to determine the zero
temperature effective potential for the corresponding condensates, and recover
the already known result for <A^2> \neq 0, together with <A_\mu
A_\nu-\delta_{\mu\nu}/d A^2>=0, a nontrivial check that the approach is
consistent with Lorentz symmetry. The formalism is such that it is readily
generalizable to the finite temperature case, which shall allow a future
analytical study of the electric-magnetic symmetry of the <A^2> condensate,
which received strong evidence from recent lattice simulations by Chernodub and
Ilgenfritz, who related their results to 3 regions in the Yang-Mills phase
diagram.
