Q-Independence of the Jimbo\u2013Drinfeld Quantization

Abstract

Let {mathrm {G}} be a connected semi-simple compact Lie group and for 0<q<1, let ({mathbb {C}}[mathrm {G]_q},varDelta _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-actions of the maximal torus.