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 (Formula presented.); with 1/2 and 1/3 for the system (Formula presented.)) 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.
Original language | English |
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Pages (from-to) | 2313-2327 |
Number of pages | 15 |
Journal | Communications in Algebra |
Volume | 52 |
Issue number | 6 |
DOIs | |
State | Published - 2024 |
Bibliographical note
Publisher Copyright:© 2024 The Author(s). Published with license by Taylor & Francis Group, LLC.
Keywords
- Automorphisms
- Chevalley groups
- commutative rings