  The correct implementation of the Loop Quantum Gravity to the early
homogeneous Universe has been the subject of a long debate in the literature
because the SU(2) symmetry cannot be properly retained. The role of this
symmetry is expressed by the Gauss constraint. Here, a non-vanishing Gauss
constraint is found. However, we show that using suitable variables, it can be
recast into three Abelian constraints, justifying the absence of such a
symmetry in Loop Quantum Cosmology.
