𝒪-operators of ternary Jordan algebras and ternary Jordan Yang–Baxter equations

Abstract

In this paper, we study the representation of ternary Jordan algebras which allows us to introduce the notion of coherent ternary Jordan algebras. Then the [Formula: see text]-operators of ternary Jordan algebras are introduced and the solutions of ternary Jordan Yang–Baxter equation are discussed involving [Formula: see text]-operators. Moreover, ternary pre-Jordan algebras are studied as the algebraic structure behind the [Formula: see text]-operators. Finally, the relations among ternary Jordan algebras and ternary pre-Jordan algebras are established and illustrated by examples.