Drinfeld Realization of Affine Quantum Algebras: The Relations

In this paper the structure of the Drinfeld realization ${\text{Udr}}_q$ of affine quantum algebras (both untwisted and twisted) is described in details, and its defining relations are studied and simplified. As an application, a homomorphism $\psi$ from this realization to the Drinfeld and Jimbo presentation ${\text{U}}_q^{DJ}$ is provided, and proved to be surjective.