Outer automorphisms of algebraic groups and a Skolem-Noether
theorem for Albert algebras
The question of existence of outer automorphisms of a simple
algebraic group G arises naturally both when working with the
Galois cohomology of G and as an example of the algebro-geometric
problem of determining which connected components of Aut(G)
have rational points. The existence question remains open only for four
types of groups, and we settle one of the remaining cases, type 3 D 4 .
The key to the proof is a Skolem-Noether theorem for cubic etale
subalgebras of Albert algebras which is of independent interest. Necessary
and sufficient conditions for a simply connected group of outer type A
to admit outer automorphisms of order 2 are also given.
(This paper has appeared in Documenta Math. 21 (2016), 917-954)
Skip Garibaldi < skip@member.ams.org >
Holger P. Petersson < holger.petersson@fernuni-hagen.de >