Let $ U_q(\mathfrak{g})$ (defined over $ \mathbb{C}(q)$ ) be the quantized universal enveloping algebra of a simple Lie algebra $ \mathfrak{g}$ . Let $ M$ a finite-dimensional simple left $ U_q(\mathfrak{g})$ -module. Is it true that $ \dim_{\mathbb{C}(q)}\mathrm{End}_{U_q(\mathfrak{g})}(M)=1$ ? How to sketch a proof? The problem is that the field $ \mathbb{C}(q)$ is not algebraicallyRead more