On the solutions of the Yang-Baxter equations

Abstract

Classification of triangular constant solutions oft he Yang-Baxter equation is done. The formulas for the baxterization of braid group representations are used for finding trigonometric solutions of the Yang-Baxter equations from the constant ones. Some of the obtained solutions correspond to knows solutions but several new noes are obtained as well. The calculations confirm that the baxterization formulas for more then two eigenvalues of the $\hat{R}$-matrix are not universal. The relationship between recently published representation of the coloured braid group and solutions found before is described.