On a ternary generalization of Jordan algebras

Based on the relation between the notions of Lie triple systems and Jordan algebras, we introduce the n-ary Jordan algebras, an n-ary generalization of Jordan algebras obtained via the generalization of the following property Rx,Ry∈DerA, where A is an n-ary algebra. Next, we study a ternary example of these algebras. Finally, based on the construction of a family of ternary algebras defined by means of the Cayley–Dickson algebras, we present an example of a ternary Dx,y-derivation algebra (n-ary Dx,y-derivation algebras are the non-commutative version of n-ary Jordan algebras).

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