$. The isotropic model $\Delta = \pm1$ is invariant under the rotation group $SU(2)$, but as long as $|\Delta| \neq 1$ this symmetry is broken down to the rotation group $U(1)$ around the z-axis. One can “restore" this full rotation symmetry by adding appropriate boundary operators to the Hamiltonian of the open chain. The classical group $SU(2)$ becomes then the quantum group $SU_q(2)$, where the quantum parameter is related to the anisotropy by $\Delta  = \frac{q+q^{-1}}{2}$ [@sklyanin], [@pasquier-saleur]. The “restoration" of a classical symmetry into a $q$-symmetry is achieved at the price of deforming the algebra and the corresponding addition rule of angular momentum. The $q$-sum rule, which is called the comultiplication, becomes non local and violates parity. The total raising (lowering) operators acting on the whole chain are a sum of the raising ( lowering) operators acting at every single site times a non-local term involving all the remaining sites which appear in an asymmetric way: sites located to the left or to the right at a given site contribute differently.

These features of $q$-groups made them specially well-suited to implement a RG method which takes into account the correlation between neighboring blocks. In the forthcoming sections we show 