Rational subgroups and invariants of F4

Abstract

It is known that simple algebraic groups of type F4, defined over a field k, are precisely the full automorphism groups of Albert algebras over k. For an Albert division algebra A over a field k of characteristic different from 2 and 3 and G = Aut(A), the full group of algebra automorphisms of A, it is known that any connected, simple k-subgroup of G is of type A2 or D4. In this paper, we classify all k-embeddings of connected, simple groups of type A2 and D4 in G and give Galois cohomological conditions for such embeddings to exist, along with some applications.