  Let $\mathrm G$ be a connected semi-simple compact Lie group and for $0<q<1$,
let $(\mathbb{C}[\mathrm{G]_q}],\Delta_q)$ be the Jimbo-Drinfeld
$q$-deformation of $\mathrm G$. We show that the $C^*$-completions of
$\mathrm{C}[\mathrm{G]_q}$ are isomorphic for all values of $q$. Moreover,
these isomorphisms are equivariant with respect to the right-action of the
maximal torus.
