On a ternary generalization of Jordan algebras (Preprint)

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Type: Preprint
National /International: International
Title: On a ternary generalization of Jordan algebras
Publication Date: 2017-10-23
Authors: - Ivan Kaygorodov
- Alexander P. Pozhidaev
- Paulo Saraiva
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).
Institution: DMUC 17-42
Online version: http://www.mat.uc.pt...prints/eng_2017.html
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