Drinfeld Realization of Affine Quantum Algebras: the Relations

Abstract

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