Fields of Fractions of Quantum Solvable Algebras

We introduce the notion of pure Q-solvable algebra. The quantum matrices, quantum Weyl algebra, Uq(n) are the examples. It is proved that the skew field of fractions of a pure Q-solvable algebra R is isomorphic to the skew field of twisted rational functions. This is a quantum version of the Gelfand–Kirillov conjecture for solvable algebraic Lie algebras