New R-matrices for Small Quantum Groups

It is widely accepted that small quantum groups should possess a quasitriangular structure, even though this is technically not true. In this article we construct explicit R-matrices, sometimes several inequivalent ones, over certain natural extensions of small quantum groups by grouplike elements. The extensions are in correspondence to lattices between root and weight lattice. Our result generalizes a well-known calculation for uq(𝔰𝔩2) used in logarithmic conformal field theories.