2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153467We show that the affine quantum group $U_q(\hat{sl_2})$ is isomorphic to a bicrossproduct central extension $C Z{}_χ\cross U_q(Lsl_2)$ of the quantum loop group $U_q(Lsl_2)$ by a quantum cocycle $χ$, which we construct. We prove the same result for $U_q(\hat{g})$ in R-matrix form.LATEX 10 pagesQuantum Algebratext