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

Key Points

• The aim is to construct an equivariant map involving the exceptional Jordan algebra and to explore its structure constants and isotopes.
• Constructed an equivariant map from the space of pairs of exceptional Jordan algebras to Hom k (J J, J) using homogeneous polynomials of degree 8.
• Defined isotopes of the Jordan algebra using equivariant maps from the algebra to trilinear forms.
• The constructed map associates a generic point in V to the structure constant of the corresponding isotope of J.
• An alternative definition of the isotopes is provided through the relationship with trilinear forms.