Automorphisms and isomorphisms of Chevalley groups and algebras

TL;DR

This paper characterizes and explicitly describes the automorphism groups of adjoint Chevalley groups, their elementary subgroups, and associated Lie rings over rational algebras, establishing their equivalence.

Contribution

It provides a detailed description of automorphisms for Chevalley groups, elementary subgroups, and Lie rings, demonstrating their automorphism groups are identical.

Findings

Automorphism groups of Chevalley groups and related structures are explicitly determined.

Automorphisms of these groups are shown to be the same across different algebraic objects.

The results apply to groups over rational algebras of rank at least 2.

Abstract

An adjoint Chevalley group of rank at least 2 over a rational algebra (or a similar ring), its elementary subgroup, and the corresponding Lie ring have the same automorphism group. These automorphisms are explicitly described.