Classification of real trivectors in dimension nine

In this paper we classify real trivectors in dimension 9. The corresponding classification over the field C of complex numbers was obtained by Vinberg and Elashvili 1978. One main tools used for their construction representation SL(9,C) on space C9 as a theta-representation to Z/3Z-grading simple Lie algebra type E8. This divides into three groups: nilpotent, semisimple, mixed trivectors. Our follows same pattern. We use Galois cohomology, first second, obtain R.