Standardness and Standard Automorphisms of Chevalley Groups, I: the Case of Rank at Least Two

The author studies the linkage between the standardness and the standard automorphisms of Chevalley groups over rings. It is proved that if H is any standard subgroup of G(R), then each of its automorphisms can be extended to an automorphism of G(R, I), restricted to an automorphism of E(R, I), and an automorphism of E(R, I) can be extended to one of G(R, I). The case of Chevalley groups of rank at least two is treated in this paper. Further results about the case of Chevalley groups of rank one, the case of non-commutative ground ring and some others exceptions will appear elsewhere.