Triangular Dynamical r-Matrices and Quantization

AbstractWe study some general aspects of triangular dynamical r-matrices using Poisson geometry. We show that a triangular dynamical r-matrix r:h*→∧2g 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]]