What question did this study set out to answer?

The aim is to construct an equivariant map involving the exceptional Jordan algebra and to explore its structure constants and isotopes.

April 4, 2026Open Access

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.

Abstract

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.

اسأل الذكاء الاصطناعي

Bookmark

View Full Paper