Automorphisms of Chevalley groups of types \(B_2\) and \(G_2\) over local rings. (Q2519210)

Let \(R\) be a local ring with a unit. In this paper, by generalizing some methods of \textit{V. M. Petechuk} [Mat. Zametki 28, 187-204 (1980; Zbl 0437.20037)], consider every Chevalley group as embedded into the group \(\text{GL}_n(R)\) for some \(n\in\mathbb{N}\), and consider Chevalley groups as matrix groups, the author proves that every automorphism of any adjoint Chevalley group of type \(B_2\) or \(G_2\) is standard, i.e., it is a composition of an inner automorphism, a ring automorphism, and a central automorphism.