Solutions of the Yang-Baxter equation

Abstract

We give the basic definitions connected with the Yang-Baxter equation (factorization condition for a multiparticle S-matrix) and formulate the problem of classifying its solutions. We list the known methods of solution of the Y-B equation, and also various applications of this equation to the theory of completely integrable quantum and classical systems. A generalization of the Y-B equation to the case ofZ₂-graduation is obtained, a possible connection with the theory of representations is noted. The supplement contains about 20 explicit solutions.