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We can recast the Yang-Baxter equation as a triple product equation. Assumingthe triple product to satisfy some algebraic relations, we can find newsolutions of the Yang-Baxter equation. This program has been completed here forthe simplest triple systems which we call octonionic and quaternionic. Thesolutions are of rational type.Comment: 29 page

Triple products and Yang–Baxter equation. I. Octonionic and quaternionic triple systems