| Résume | On the affine quantum algebras $U_q$ Drinfeld introduced a coproduct $\Delta$ with values in a completion $V$ of the tensor product $U_q\otimes U(q)$ (in particular it is different from the standard coproduct defined on the generators $E_i, F_i, K_i^{\pm 1}$, which has values in $U_q\otimes U_q$). The Drinfeld coproduct is defined on the Drinfeld generators $X_{i,r}^{\pm}, H^{i,r}, C^{\pm 1}, K_i^{\pm 1}$, but has not yet been proved to be well defined in the general case. In this talk we prove that it is well defined both on the affine quantum algebras and on the quantum affinizations, where it is the only coproduct since the standard one is not defined. The proof depends on the study of some (well defined) derivations of a subalgebra of $V$. |
