Quantization conjecture for classical dynamical r-matrices

Let $\mathfrak h$ be the Lie algebra occurring in the classical dynamical Yang–Baxter equation, let $V$ be the representation space, and let a classical dynamical $r$-matrix be a meromorphic function

$$r:\mathfrak h^*\to \operatorname{End}_{\mathfrak h}(V\otimes V)$$

satisfying the classical dynamical Yang–Baxter equation. A quantization is a family of solutions of the quantum dynamical Yang–Baxter equation with step $\hbar$ whose expansion is $1-\hbar r(\lambda)+O(\hbar^2)$. Quantization conjecture for classical dynamical $r$-matrices. Any classical dynamical $r$-matrix can be quantized. This conjecture is proved in the non-dynamical case, and in the dynamical case for skew-symmetric solutions satisfying additional technical assumptions; the general claim is therefore solved only in the qualified cases described in the source.