Triangular dynamical r-matrices and quantization

We study some general aspects of triangular dynamical r-matrices using Poisson geometry. We show that a triangular dynamical r-matrix r: h* → ∧² g always gives rise to a regular Poisson manifold. Using the Fedosov method, we prove that non-degenerate triangular dynamical r-matrices (i.e., those such that the corresponding Poisson manifolds are symplectic) are quantizable and that the quantization is classified by the relative Lie algebra cohomology H²(g, h) ℏ.