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We give a uniform trigonometric R-matrix for the adjoint representations on the exceptional series. The exceptional series is a finite list of points on a projective line with a simple Lie algebra attached to each point. This list of Lie algebras includes the five exceptional Lie algebras. For L a simple Lie algebra there is a rational R-matrix in EndL (² (L I) ) which has a quantum deformation to a trigonometric R-matrix. We construct a sixteen dimensional algebra, A^ (2), which interpolates the quantum deformations of the algebras EndL (² (L I) ) and a 287 dimensional algebra, A^ (3), which interpolates the quantum deformations of the algebras EndL (³ (L I) ). Then we construct an R-matrix in A^ (2) which satisfies the Yang--Baxter equation in A^ (3) and which interpolates the trigonometric R-matrices for the points in the exceptional series.
Westbury et al. (Mon,) studied this question.