Automorphisms of Chevalley groups of different types over commutative rings

2011/08/02 by E. I. Bunina, Elena Bunina, Bunina, Elena · 2 citations
Mathematics · #33D80 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA) #math.GR #math.RA #msc:33D80

paper · pdf · doi:10.48550/arxiv.1108.0529

23 pages

arxiv created 2011/08/02 · openalex publication_date 2011/08/02 · arxiv updated 2011/08/03 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

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 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.

Citations

• Automorphisms of Chevalley groups of type B_l over local rings with 1/2
• Automorphisms of Chevalley groups of type F₄ over local rings with 1/2
• Automorphisms of elementary adjoint 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

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