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

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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 $B_A(x,\overline{y}^\sim,z)$.

Detaljer

Författare
  • Daniel Mondoc
Externa organisationer
  • External Organization - Unknown
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Sidor (från-till)3801-3815
TidskriftCommunications in Algebra
Volym34
Utgåva nummer10
StatusPublished - 2006
PublikationskategoriForskning
Peer review utfördJa
Externt publiceradJa