On Equivariant Maps Related to the Space of Pairs of Exceptional Jordan Algebras

Let J be the exceptional Jordan algebra and V = J J .We construct an equivariant map from V to Hom k (J J , J ) defined by homogeneous polynomials of degree 8 such that if x V is a generic point, then the image of x is the structure constant of the isotope of J corresponding to x.We also give an alternative way to define the isotope corresponding to a generic point of J by an equivariant map from J to the space of trilinear forms.