Quantum R-matrices and factorization problems (Q922632)

It is well known that there exist connections between the classical r- matrix and certain factorization problems in Lie groups. The authors establish a similar relation between the quantum R-matrix and a certain factorization problem in Hopf algebras. They introduce the notion of factorizable Hopf algebra and prove that the double of a Hopf algebra is a factorizable Hopf algebra. Finally the authors give a definition of dressing transformation in the quantum case.