# Structurable algebras and models of compact simple Kantor triple systems defined on tensor products of composition algebras

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## Abstract

Let $(A,^−)$ be a structurable algebra. Then the opposite algebra $(A^{op},^−)$ is structurable, and we show that the triple system $B_A^{op}(x,y,z):=V_{x,y}^{op}(z)=x(\overline y z)+z(\overline y x)−y(\overline x z),x,y,z\in A$, is a Kantor triple system (or generalized Jordan triple
system of the second order) satisfying the condition $(A)$. Furthermore, if $A=\mathbb{A}_1\otimes\mathbb{A}_2$
denotes tensor products of composition algebras, $(^-)$ is the standard conjugation, and $(^\land)$ denotes a certain pseudoconjugation on $A$, we show that the triple systems
$B_{\mathbb{A}_1\otimes\mathbb{A}_2}^{op}(x,\overline{y}^\land,z)$ are models of compact Kantor triple systems. Moreover these triple systems are simple if \$(dim\mathbb{A}_1,dim\mathbb{A}_2)\neq(2,2). In addition, we obtain an explicit formula for the canonical trace form for compact Kantor triple systems defined on tensor products of composition algebras.

## Detaljer

Författare
• Daniel Mondoc
Externa organisationer
• External Organization - Unknown
Forskningsområden

• Matematik

### Nyckelord

Originalspråk engelska 549-558 Communications in Algebra 33 2 Published - 2005 Forskning Ja Ja