From the Drinfeld Realization to the Drinfeld–Jimbo Presentation of Affine Quantum Algebras: Injectivity

Abstract

The surjective homomorphism $\psi$ (see [Da1]) from the Drinfeld realization $U_q^{Dr}$ to the Drinfeld and Jimbo presentation ${\mathcal{U}}_q^{DJ}$ of affine quantum algebras is proved to be injective. A consequence of the arguments used in the paper is the triangular decomposition of the Drinfeld realization of affine quantum algebras also in the twisted case. A presentation of affine Kac–Moody algebras in terms of “Drinfeld generators” is also provided.