On compact realifications of exceptional simple Kantor triple systems

Daniel MONDOC

Abstract

Let A be the realification of the matrix algebra determined by Jordan algebra of hermitian matrices of order three over a complex composition algebra. We define an involutive automorphism 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