Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras

  • Skip Garibaldi

  • Holger P. Petersson

Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras cover
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Abstract

The question of existence of outer automorphisms of a simple algebraic group GG arises naturally both when working with the Galois cohomology of GG and as an example of the algebro-geometric problem of determining which connected components of Aut(G)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 ^3DD_4. The key to the proof is a Skolem-Noether theorem for cubic étale subalgebras of Albert algebras which is of independent interest. Necessary and sufficient conditions for a simply connected group of outer type AA to admit outer automorphisms of order 2 are also given.

Cite this article

Skip Garibaldi, Holger P. Petersson, Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras. Doc. Math. 21 (2016), pp. 917–954

DOI 10.4171/DM/549