Point spaces in exceptional quadratic Jordan algebras

Abstract

The point spaces of the exceptional quadratic Jordan algebra H( O 3, J γ ), O an octonion algebra, are studied. Two such spaces B 1 , B 2 are in the same class with respect to the automorphism group Aut J (respectively, the structure group Str J ) if B 1 = B 2φ for some φ ϵ Aut J (φ ϵ Str J ). Representatives for these equivalence classes are obtained.