Automorphisms of Chevalley groups of different types over commutative rings

TL;DR

This paper proves that all automorphisms of elementary adjoint Chevalley groups of rank greater than one over certain commutative rings are standard, composed of known automorphism types, extending understanding of their symmetry structures.

Contribution

It establishes that automorphisms of these Chevalley groups are all standard, generalizing previous results to broader classes over rings with specific invertible elements.

Findings

Automorphisms are standard for Chevalley groups of rank > 1 over specified rings.

Automorphisms decompose into ring, inner, central, and graph automorphisms.

Results apply to groups with root systems of types A2, F4, B_l, C_l, G_2.

Abstract

In this paper we prove that every automorphism of (elementary) adjoint Chevalley group with root system of rank $>1$ over a commutative ring (with 1/2 for the systems $A_2$, $F_4$, $B_l$, $C_l$; with 1/2 and 1/3 for the system $G_2$) is standard, i.\,e., it is a composition of ring, inner, central and graph automorphisms.