On a ternary generalization of Jordan algebras
| Autor: | Kaygorodov, Ivan, Pozhidaev, Alexander, Saraiva, Paulo |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1080/03081087.2018.1443426 |
| Popis: | 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 $\left[ R_{x},R_{y}\right] \in Der\left( \mathcal{A}\right)$, where $\mathcal{A}$ 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). Comment: 17 pages |
| Databáze: | arXiv |
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