q-Independence of the Jimbo-Drinfeld Quantization

Abstract

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