New preprint on outer automorphisms of simple groups

New preprint out today: Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras, written with Holger P. Petersson.  In it, we study the question of existence of outer automorphisms of simple algebraic groups.  One knows that the *-action and the Tits class provide obstructions to the existence of outer automorphisms, and the question is whether they are the only obstruction.  That is, if the obstructions vanish, does there necessarily exist a corresponding outer automorphism, equivalently, a rational point on the corresponding non-identity component of the automorphism group (viewed as a variety)?  For semisimple groups, the answer is easily seen to be “no”, but for simple groups so far the answer is “yes” in all cases where we know it.  There were four remaining classes of simple groups for which the answer was unknown, and one of our main results is to settle one of those four cases, the trialitarian groups.