@UNPUBLISHED{publication1, title = "On a ternary generalization of Jordan algebras", author = "{KAYGORODOV, Ivan} and {POZHIDAEV, Alexander P.} and {SARAIVA, Paulo}", year = "2017-10-23", abstract = "Based on the relation between the notions of Lie triple system and Jordan algebra, we introduce n-ary Jordan algebras, an n-ary generalization of Jordan algebras obtained via the generalization of the following property [Rx,Ry] \∈ Der(A), where A is an n-ary algebra. Next, we study such ternary algebras. Finally, based on the construction of a family of ternary algebras defined by means of the Cayley-Dickson algebras, we present a ternary Dx,y-derivation algebra (n-ary Dx,y-derivation algebras are non-commutative version of n-ary Jordan algebras). ", url = "http://www.mat.uc.pt/preprints/eng\_2017.html", note = "" }