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

(2005) In Communications in Algebra 33(2). p.549-558
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... (More)
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 $(dim\mathbb{A}_1,dim\mathbb{A}_2)\neq(2,2). In addition, we obtain an explicit formula for the canonical trace form for compact Kantor triple systems defined on tensor products of composition algebras. (Less) Please use this url to cite or link to this publication: author publishing date type Contribution to journal publication status published subject keywords structurable algebras, composition algebras, Kantor triple systems in Communications in Algebra volume 33 issue 2 pages 549 - 558 publisher Taylor & Francis external identifiers • scopus:27944491961 ISSN 0092-7872 DOI 10.1081/AGB-200047437 language English LU publication? no id a53bf06c-80c0-425e-b4fe-f24a43d3a139 (old id 1670181) date added to LUP 2010-09-17 15:08:22 date last changed 2018-01-07 05:12:51 @article{a53bf06c-80c0-425e-b4fe-f24a43d3a139, abstract = {Let$(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$, is a Kantor triple system (or generalized Jordan triple<br/><br> system of the second order) satisfying the condition$(A)$. Furthermore, if$A=\mathbb{A}_1\otimes\mathbb{A}_2$<br/><br> denotes tensor products of composition algebras,$(^-)$is the standard conjugation, and$(^\land)$denotes a certain pseudoconjugation on$A$, we show that the triple systems<br/><br>$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.},
author       = {Mondoc, Daniel},
issn         = {0092-7872},
keyword      = {structurable algebras,composition algebras,Kantor triple systems},
language     = {eng},
number       = {2},
pages        = {549--558},
publisher    = {Taylor & Francis},
series       = {Communications in Algebra},
title        = {Structurable algebras and models of compact simple Kantor triple systems defined on tensor products of composition algebras},
url          = {http://dx.doi.org/10.1081/AGB-200047437},
volume       = {33},
year         = {2005},
}