Let $U_q(\mathfrak{g})$ be the quantized enveloping algebra of a complex semisimple Lie algebra and let $\mathcal{O}_q(G)$ be the quantized coordinate algebra of the corresponding simply-connected group $G$. It is well known that $\mathcal{O}_q(G)$ is Noetherian, by using $R$-matrices to get certain relations between generators (see for example the book "Lectures on Algebraic Quantum Groups" by Brown and Goodearl, chapter 8).
My question is: is it known whether the integral form of $\mathcal{O}_q(G)$ is also Noetherian? Here by integral form I mean the dual Hopf algebra of Lusztig's integral form of $U_q(\mathfrak{g})$. The only thing I found in that direction is in the Inventiones paper "Representations of quantum algebras." by Andersen, Polo, and Kexin. In Polo's appendix (section 12) it is proved that, in type $A$, the integral form of the quantized coordinate algebra is given by the usual generators and relations for quantum $SL_n$. This immediately implies that it is Noetherian. Does anyone know of similar results in other types?
