On the constructions of Tits and Faulkner: an isomorphism theorem

Abstract

Classification theory guarantees the existence of an isomorphism between any two E8's, at least over an algebraically closed field of characteristic 0. The purpose of this paper is to construct for any Jordan algebra J of degree 3 over a field Φ of characteristic ≠2,3 an explicit isomorphism between the algebra obtained from J by Faulkner's construction and the algebra obtained from the split octonions and J by Tits construction.