Automorphisms of Chevalley groups of different types over commutative rings

E. I. Bunina

doi:10.1016/j.jalgebra.2012.01.002

Automorphisms of Chevalley groups of different types over commutative rings

E. I. Bunina

Lomonosov Moscow State University

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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 A ₂, F ₄, B _l, C _l; with 1/2 and 1/3 for the system G ₂) is standard, i.e., it is a composition of ring, inner, central and graph automorphisms.

Original language	English
Pages (from-to)	154-170
Number of pages	17
Journal	Journal of Algebra
Volume	355
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2012.01.002
State	Published - 1 Apr 2012
Externally published	Yes

Keywords

Adjoint groups
Automorphisms
Chevalley groups over rings
Isomorphisms

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10.1016/j.jalgebra.2012.01.002

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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 A 2, F 4, B l, C l; with 1/2 and 1/3 for the system G 2) is standard, i.e., it is a composition of ring, inner, central and graph automorphisms.",

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AB - 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 A 2, F 4, B l, C l; with 1/2 and 1/3 for the system G 2) is standard, i.e., it is a composition of ring, inner, central and graph automorphisms.

KW - Adjoint groups

KW - Automorphisms

KW - Chevalley groups over rings

KW - Isomorphisms

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Automorphisms of Chevalley groups of different types over commutative rings

Abstract

Keywords

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