Classification of R-operators

We classified the R-operators which satisfy the quantum Yang-Baxter equatio n on a function space. In this study, we gave all the meromorphic solutions of the system of the functional equations which is a necessary and suffici ent condition for the R-operator to satisfy the Yang-Baxter equation. Most of the solutions were expressed in terms of the elliptic, trigonometric and rational functions. (C) 2001 American Institute of Physics.