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