The universal R-matrix and its associated quantum algebra as functionals   of the classical r-matrix: the $sl_{2}$ case
  Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ and its universal quantum $R$-matrix are explicitely constructed as functionals of the associated classical $r$-matrix. In this framework, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ is naturally imbedded in the universal envelopping algebra of the $sl_{2}$ current algebra. 
Laurent Freidel and J. M. Maillet