Towards an explicit expression of the Seiberg-Witten map at all orders

The Seiberg-Witten map links non-commutative gauge theories to ordinary gauge theories, and allows to express the non-commutative variables in terms of the commutative ones. Its explicit form can be found order by order in the non-commutative parameter theta and the gauge potential A by the requirement that gauge orbits are mapped on gauge orbits. This of course leaves a biguities, corresponding to gauge transformations, and there is an infinity of solutions. Is there one better, clearer than the others? In the abelian case, we were able to find a solution, linked by a gauge transformation to already known formulas, which has the property of admitting a recursive formulation, uncovering some pattern in the map. In the special case of a pure gauge, both abelian and non abelian, these expressions can be summed up, and the transformation is expressed using the parametrisation in terms of the gauge group.