Quantization of geometric classical $\mbox{r}$-matrices

Abstract

In this note we define geometric classical r-matrices and quantum R-matrices, and show how any geometric classical r-matrix can be quantized to a geometric quantum R-matrix. This is one of the simplest nontrivial examples of quantization of solutions of the classical Yang-Baxter equation, which can be explicitly computed. The idea of the above quantization was inspired by the results in [ESS]. We note that a construction similar to ours was obtained in [KLM].