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

Mondoc, Daniel LU (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)
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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
2017-01-01 04:25:21
@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},
}