  Let $\mathbb K$ be a field and suppose $p, q\in\mathbb K^*$ are not roots of
unity. We prove that the two quantum groups $U_q(\mathfrak {sl}_{n+1})$ and
$U_p(\mathfrak{sl}_{n+1})$ are isomorphic as $\mathbb K$-algebras implies that
$p=\pm q^{\pm 1}$ when $n$ is even. This new result answers a classical
question of Jimbo.
