Automorphisms of elementary adjoint Chevalley groups of types $A_l, D_l, E_l$ over local rings with 1/2

TL;DR

This paper proves that automorphisms of elementary adjoint Chevalley groups of types A_l, D_l, E_l over local rings with 1/2 are essentially composed of ring automorphisms and conjugations, clarifying their structure.

Contribution

It establishes a complete description of automorphisms for these Chevalley groups over local rings with 1/2, showing they are generated by ring automorphisms and conjugations.

Findings

Automorphisms are compositions of ring automorphisms and conjugations.

Automorphisms are characterized explicitly for types A_l, D_l, E_l.

Results hold over local rings with 1/2.

Abstract

In the paper we prove that every automorphism of and elementary adjoint Chevalley group of types $A_l, D_l$, or $E_l$, over local commutative ring with 1/2 is a composition of a ring automorphism and conjugation by some matrix from the normalizer of the Chevalley group in $\GL(V)$ ($V$ is the adjoint representation space).