Quantum solvable algebras. Ideals and representations at roots of 1

There studed correspondence between symplectic leaves, irreducible representations and prime ideals, which is invariant with respect to quantum adjoint action. The Conjecture of De Concini-Kac-Procesi on dimensions of irreducible representations is proved for sufficiently great $l$.Comment: Latex, 24 page

Fields of fractions of quantum solvable algebras

We introduce the notion of pure Q-solvable algebra. The quantum matrices, quantum Weyl algebra, U_q(n) are the examples. It is proved that the skew field of fractions of pure Q-solvable algebra is isomorphic to the skew field of twisted rational functions. This is the quantum version of Gelfand-Kirillov conjecture for solvable algebraic Lie algebras.Comment: Latex, 9 page