Let A be the realification of the
matrix algebra determined by Jordan algebra of hermitian matrices of order
three over complex composition algebra. We define an in volutive auto morphism on A with a certain action on the triple system obtained from A which give models of simple compact Kantor triple systems. In addition, we give an explicit
formula for the canonical trace form and the classification for these triples
and their corresponding exceptional real simple Lie algebras. Moreover, we
present all realifications of complex exceptional simple Lie algebras as Kantor
algebras for a compact simple Kantor triple system defined on a structurable
algebra of skew-dimension one.
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