On a ternary generalization of Jordan algebras

Ivan Kaygorodov, Alexander Pozhidaev, Paulo Saraiva

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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 (R x , R y )∈ Der(A) 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 D x,y -derivation algebra (n-ary D x,y -derivation algebras are the non-commutative version of n-ary Jordan algebras).

Original languageEnglish
Pages (from-to)1074-1102
Number of pages29
JournalLinear and Multilinear Algebra
Issue number6
Publication statusPublished - 3 Jun 2019


  • Cayley–Dickson construction
  • derivations
  • generalized Lie algebras
  • Jordan algebras
  • Lie triple systems
  • n-ary algebras
  • non-commutative Jordan algebras
  • TKK construction
  • 17C50
  • 17A42
  • LIE
  • Cayley-Dickson construction


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