Geodesic
On the Automorphisms of Infinite Chevalley Groups
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 908-911

Voir la notice de l'article provenant de la source Cambridge University Press

In (8, § 3.2) Steinberg proved the following result.THEOREM. Let K be a finite field, G′ a simple Chevalley group (“normal type1’) over K. Then every automorphism of G’ is the composite of inner, graph, field, and diagonal automorphisms.For the meaning of these notions, see (8). Our aim in this note is to indicate how the Theorem may be extended to arbitrary infinite fields K, provided we replace G′ by the group denoted G in (5) and ĝ in (8). This amounts to proving the Theorem for automorphisms of G′ which are induced by automorphisms of G; when K is finite, Steinberg's results show that all automorphisms of G′ arise in this way. As Steinberg points out, the sole use made of the finiteness of K in his argument is in the proof of the following statement: Let U be the subgroup of G′ corresponding to the set of positive roots, and let σ be any automorphism of G′; then Uσ is conjugate to U in G′. 
Humphreys, J. E. On the Automorphisms of Infinite Chevalley Groups. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 908-911. doi: 10.4153/CJM-1969-099-7
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