Automorphisms of Chevalley groups over commutative rings

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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 languageEnglish
Pages (from-to)2313-2327
Number of pages15
JournalCommunications in Algebra
Issue number6
StatePublished - 2024


  • Automorphisms
  • Chevalley groups
  • commutative rings

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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