Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/89485
 Title: On a ternary generalization of Jordan algebras Authors: Kaygorodov, IvanPozhidaev, AlexanderSaraiva, 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). URI: http://hdl.handle.net/10316/89485 DOI: 10.1080/03081087.2018.1443426 Rights: embargoedAccess Appears in Collections: I&D CMUC - Artigos em Revistas Internacionais

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