Rational forms of exceptional dual pairs

Let gg be a simple Lie algebra of type F4F4 or EnEn defined over a local or global field k   of characteristic zero. We show that gg can be obtained by the Tits construction from an octonion algebra OO and a cubic Jordan algebra JJ. In particular, gg contains a dual pair hh defined over k   which is the direct sum of the derivation algebras of OO and JJ. We determine the conjugacy classes of k  -forms of hh in gg.