Structurable algebras and models of compact simple Kantor triple systems defined on tensor products of composition algebras

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

Abstract

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
system of the second order) satisfying the condition $(A)$. Furthermore, if $A=\mathbb{A}_1\otimes\mathbb{A}_2$
denotes tensor products of composition algebras, $(^-)$ is the standard conjugation, and $(^\land)$ denotes a certain pseudoconjugation on $A$, we show that the triple systems
$B_{\mathbb{A}_1\otimes\mathbb{A}_2}^{op}(x,\overline{y}^\land,z)$ 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.

Detaljer

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

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematik

Nyckelord

Originalspråkengelska
Sidor (från-till)549-558
TidskriftCommunications in Algebra
Volym33
Utgåva nummer2
StatusPublished - 2005
PublikationskategoriForskning
Peer review utfördJa
Externt publiceradJa