Automorphisms of Chevalley groups over commutative rings

2023/04/26 by E. I. Bunina, Bunina, Elena · 2 citations
Mathematics · #20G07 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2304.13447

openalex publication_date 2023/04/26 · openalex created_date 2023/04/28 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that every automorphism of a Chevalley group (or its elementary subgroup) with root system of rank >1 over a commutative ring (with 1/2 for the systems A₂, F₄, B_l, C_l; with 1/2 and 1/3 for the system G₂) is standard, i.e., it is a composition of ring, inner, central and graph automorphisms. This result finalizes description of automorphisms of Chevalley groups. However the restrictions on invertible elements can be a topic of further considerations. We provide also some model-theoretic applications of this description.

Cited by

• Abstract isomorphisms of isotropic root graded groups over rings
• Automorphisms of Twisted Chevalley Groups of type ² D_ℓ (ℓ ≥ 4) over Local Rings

Related

• Automorphisms of Chevalley groups of different types over commutative rings
• Automorphisms of a Chevalley group of type G₂ over a commutative ring R with 1/3 generated by the all invertible elements and 2R
• Automorphisms of Chevalley groups of types A_l, D_l, E_l over local rings with 1/2
• Automorphisms of Chevalley groups of types A_l, D_l, E_l over local rings without 1/2
• Automorphisms of Chevalley groups of types B₂ and G₂ over local rings