Models of compact simple Kantor triple systems defined on a class of structurable algebras of skew-dimension one
(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:
https://lup.lub.lu.se/record/1670178
- author
- Mondoc, Daniel LU
- publishing date
- 2006
- 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
- 2022-01-26 21:11:41
@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}}, }