Quantum dynamical R-matrices and quantum Frobenius group

We propose an algebraic scheme for quantizing the rational Ruijsenaars-Schneider model in the R-matrix formalism. We introduce a special parametrization of the cotangent bundle over GL(N, C). In new variables the standard symplectic structure is described by a classical (Frobenius) tau-matrix and by a new dynamical <(tau)over bar>-matrix. Quantizing both of them we find the quantum L-operator algebra and construct its particular representation corresponding to the rational Ruijsenaars-Schneider system. Using the dual parametrization of the cotangent bundle we also derive the algebra for the L-operator of the hyperbolic Calogero-Moser system.