| Title | Models of compact simple Kantor triple systems defined on a class of structurable algebras of skew-dimension one |
| Authors | Daniel Mondoc |
| Alternative Location | http://dx.doi.org/10.1080/0..., Restricted Access |
| Publication | Communications in Algebra |
| Year | 2006 |
| Volume | 34 |
| Issue | 10 |
| Pages | 3801 - 3815 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Taylor & Francis, Inc. |
| Abstract English | 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 $B_A(x,\overline{y}^\sim,z)$. |
| Keywords | structurable algebras, composition algebras, Kantor triple systems, |
| ISBN/ISSN/Other | ISSN: 1532-4125 (online) |
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