Geodesic
Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras
Documenta mathematica, Tome 21 (2016), pp. 917-954.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 étale 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.
Classification : 20G41, 11E72, 17C40, 20G15 
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     author = {Garibaldi, Skip and Petersson, Holger P.},
     title = {Outer automorphisms of algebraic groups and a {Skolem-Noether} theorem for {Albert} algebras},
     journal = {Documenta mathematica},
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     publisher = {mathdoc},
     volume = {21},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a19/}
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Garibaldi, Skip; Petersson, Holger P. Outer automorphisms of algebraic groups and a Skolem-Noether theorem for Albert algebras. Documenta mathematica, Tome 21 (2016), pp. 917-954. http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a19/