Unrestricted Quantum Moduli Algebras, II: Noetherianity and Simple Fraction Rings at Roots of 1

We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and complex semisimple Lie algebra g are Noetherian rings and finitely generated rings over C (q). Moreover, we show that these two properties still hold on C, q^-1 for the integral version of the quantum graph algebra. We also study the specializations L₀, ₍^ of the quantum graph algebra at a root of unity of odd order, and show that L₀, ₍^ and its invariant algebra under the quantum group U_ (g) have classical fraction algebras which are central simple algebras of PI degrees that we compute.