| Title | Structurable algebras and models of compact simple Kantor triple systems defined on tensor products of composition algebras |
| Authors | Daniel Mondoc |
| Alternative Location | http://dx.doi.org/10.1081/A..., Restricted Access |
| Publication | Communications in Algebra |
| Year | 2005 |
| Volume | 33 |
| Issue | 2 |
| Pages | 549 - 558 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Taylor & Francis, Inc. |
| Abstract English | 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> system of the second order) satisfying the condition $(A)$. Furthermore, if $A=\mathbb{A}_1\otimes\mathbb{A}_2$<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> $B_{\mathbb{A}_1\otimes\mathbb{A}_2}^{op}(x,\overline{y}^\land,z)$ 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. |
| Keywords | structurable algebras, composition algebras, Kantor triple systems, |
| ISBN/ISSN/Other | ISSN: 1532-4125 (online) |
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