Automorphisms of a Chevalley group of type G_2 over a commutative ring R with 1/3 generated by the all invertible elements and 2R

TL;DR

This paper proves that all automorphisms of a Chevalley group of type G_2 over certain rings are composed of ring and inner automorphisms, under specific invertibility conditions.

Contribution

It establishes a complete description of automorphisms for G_2 Chevalley groups over rings with 1/3 invertible and 2R, showing they are generated by ring and inner automorphisms.

Findings

Automorphisms are compositions of ring and inner automorphisms.

Applicable to Chevalley groups of type G_2 over rings with 1/3 and 2R.

Extends understanding of automorphism structure in algebraic groups.

Abstract

In this paper we prove that every automorphism of a Chevalley group with the root system G_2 over a commutative ring R with 1/3, generated by all its invertible elements and the ideal 2R is a composition of ring and inner automorphisms.