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Models of compact simple Kantor triple systems defined on a class of structurable algebras of skew-dimension one

Mondoc, Daniel LU (2006) In Communications in Algebra 34(10). p.3801-3815
Abstract
Let $(A,^-):={\cal M}(J)$ be the $2 \times 2$-matrix algebra determined by Jordan algebra $J:=H_3(\mathbb{A})$ of hermitian $3 \times 3$-matrices over a real composition algebra $\mathbb{A}$, where $(A,^-)$ is the standard involution on $A$. We show that the triple systems $B_A(x,\overline{y}^\sim,z), x,y,z\in\mathbb{A}$, are models of simple compact Kantor triple systems satisfying the condition $(A)$, where $B_A(x,y,z)$ is the triple system obtained from the algebra $(A,^-)$ and $^\sim$ denotes a certain involution on $A$. In addition, we obtain an explicit formula for the canonical trace form for the triple systems $B_A(x,\overline{y}^\sim,z)$.
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
34
issue
10
pages
3801 - 3815
publisher
Taylor & Francis
external identifiers
  • scopus:33845905177
ISSN
0092-7872
DOI
10.1080/00927870600862656
language
English
LU publication?
no
id
2762dc4f-2206-4cfd-bd49-8679a5ab7013 (old id 1670178)
date added to LUP
2016-04-01 11:59:13
date last changed
2025-10-14 12:54:30
@article{2762dc4f-2206-4cfd-bd49-8679a5ab7013,
  abstract     = {{Let $(A,^-):={\cal M}(J)$ be the $2 \times 2$-matrix algebra determined by Jordan algebra $J:=H_3(\mathbb{A})$ of hermitian $3 \times 3$-matrices over a real composition algebra $\mathbb{A}$, where $(A,^-)$ is the standard involution on $A$. We show that the triple systems $B_A(x,\overline{y}^\sim,z), x,y,z\in\mathbb{A}$, are models of simple compact Kantor triple systems satisfying the condition $(A)$, where $B_A(x,y,z)$ is the triple system obtained from the algebra $(A,^-)$ and $^\sim$ denotes a certain involution on $A$. In addition, we obtain an explicit formula for the canonical trace form for the triple systems $B_A(x,\overline{y}^\sim,z)$.}},
  author       = {{Mondoc, Daniel}},
  issn         = {{0092-7872}},
  keywords     = {{structurable algebras; composition algebras; Kantor triple systems}},
  language     = {{eng}},
  number       = {{10}},
  pages        = {{3801--3815}},
  publisher    = {{Taylor & Francis}},
  series       = {{Communications in Algebra}},
  title        = {{Models of compact simple Kantor triple systems defined on a class of structurable algebras of skew-dimension one}},
  url          = {{http://dx.doi.org/10.1080/00927870600862656}},
  doi          = {{10.1080/00927870600862656}},
  volume       = {{34}},
  year         = {{2006}},
}