Models of Compact Simple Kantor Triple Systems Defined on a Class of Structurable Algebras of Skew-Dimension One

Abstract

Let (A,−): = ℳ(J) be the 2 × 2-matrix algebra determined by Jordan algebra J: = H 3(𝔸) of hermitian 3 × 3-matrices over a real composition algebra 𝔸, where (−) is the standard involution on A. We show that the triple systems B A (x, ∼,z), x,y,z ∈ 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 (∼) 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, ∼,z).