Triple Products and Yang-Baxter Equation (I): Octonionic and   Quaternionic Triple Systems
  We can recast the Yang-Baxter equation as a triple product equation. Assuming the triple product to satisfy some algebraic relations, we can find new solutions of the Yang-Baxter equation. This program has been completed here for the simplest triple systems which we call octonionic and quaternionic. The solutions are of rational type. 
S. Okubo