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:
https://lup.lub.lu.se/record/1670181
- author
- Mondoc, Daniel LU
- publishing date
- 2005
- 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
- 2016-04-01 11:39:58
- date last changed
- 2022-03-20 17:11:34
@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}}, keywords = {{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}}, doi = {{10.1081/AGB-200047437}}, volume = {{33}}, year = {{2005}}, }