Abstract
ABSTRACT Let (A, −) be a structurable algebra. Then the opposite algebra (A op , −) is structurable, and we show that the triple system B op A(x, y, z):=Vopx,y(z)=x(y¯z)+z(y¯x)−y(x¯z), x, y, z ∈ A, is a Kantor triple system (or generalized Jordan triple system of the second order) satisfying the condition (A). Furthermore, if A=𝔸1⊗𝔸2 denotes tensor products of composition algebras, (−) is the standard conjugation, and (∧) denotes a certain pseudoconjugation on A, we show that the triple systems B op 𝔸1⊗𝔸2 ( x , y¯∧, z) are models of compact Kantor triple systems. Moreover these triple systems are simple if (dim𝔸1, dim𝔸2) ≠ (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.
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