Automorphisms of Chevalley groups of different types over commutative rings

Elena Bunina

Automorphisms of Chevalley groups of different types over commutative rings

Group Theory 2011-08-03 v1 Rings and Algebras

Authors: Elena Bunina

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.

Keywords

Chevalley groups automorphisms commutative rings root systems standard automorphisms graph automorphisms

Cite

@article{arxiv.1108.0529,
  title  = {Automorphisms of Chevalley groups of different types over commutative rings},
  author = {Elena Bunina},
  journal= {arXiv preprint arXiv:1108.0529},
  year   = {2011}
}

Comments

23 pages

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