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 YangâBaxter 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.
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