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Title: On a ternary generalization of Jordan algebras
Authors: Kaygorodov, Ivan
Pozhidaev, Alexander
Saraiva, Paulo
Keywords: Jordan algebras; non-commutative Jordan algebras; derivations; n-ary algebras; Lie triple systems; generalized Lie algebras; Cayley–Dickson construction; TKK construction
Issue Date: 2019
Publisher: Taylor & Francis
Project: UID/MAT/00324/2019 
Serial title, monograph or event: Linear and Multilinear Algebra
Volume: 67
Issue: 6
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 [R_x; R_y] \in 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).
DOI: 10.1080/03081087.2018.1443426
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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