The universal R-matrix and its associated quantum algebra as functionals of the classical r-matrix: the $s{l}_2$ case

Laurent Freidel, J. M. Maillet

Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra ${\mathcal{U}}_{\hslash }(s{l}_2)$ and its universal quantum $R$-matrix are explicitely constructed as…