  We develop algebraic methods for finding loop corrections to the N=4 SYM
dilatation generator, within the noncompact psu(1,1|2) sector. This sector
gives a 't Hooft coupling lambda-dependent representation of psu(1,1|2) times
psu(1|1)^2. At first working independently of the representation, we present an
all-order algebraic ansatz for the lambda-dependence of this Lie algebra's
generators. The ansatz solves the symmetry constraints if an auxiliary
generator, h, satisfies certain simple commutation relations with the Lie
algebra generators. Applying this to the psu(1,1|2) sector leads to an
iterative solution for the planar three-loop dilatation generator in terms of
leading order symmetry generators and h, which passes a thorough set of
spectral tests. We argue also that this algebraic ansatz may be applicable to
the nonplanar theory as well.
