Abstract
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 where
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
-derivation algebra (n-ary
-derivation algebras are the non-commutative version of n-ary Jordan algebras).
Acknowledgements
The authors are thankful to the referee for the valuable remarks.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
FEUC, Universidade de Coimbra, Coimbra, Portugal. CeBER, Universidade de Coimbra, Coimbra, Portugal.