On the Gelfand-Kirillov conjecture for quantum algebras

Let $q$ be a complex not a root of unity and $\mathfrak{g}$ be a semi-simple Lie $\mathbb{C}$-algebra. Let $U_{q}(\mathfrak{g})$ be the quantized enveloping algebra of Drinfeld and Jimbo, $U_{q}(\mathfrak{n}^-)\otimes U^{0}\otimes U_{q}(\mathfrak{n})$ be its triangular decomposition, and $\mathbb{C}_{q}[G]$ the associated quantum group. We describe explicitly $\operatorname{Fract} U_{q}(\mathfrak{n})$ and $\operatorname{Fract}\mathbb{C}_{q}[G]$ as a quantum Weyl field. We use for this a quantum analogue of the Taylor lemma.