R-matrix structures for classical and quantum Ruijsenaars-Schneinder models

We use the reduction approach to derive a hamiltonian structure of the classical spin hyperbolic Ruijsenaars-Schneinder model. We show that the model enjoys the Poisson-Lie symmetry which explains its superintegrability. For the quantum model without spin we obtain the L-operator algebra and integrals of motion in the R-matrix formalism.