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arXiv · 2304.13447

Automorphisms of Chevalley groups over commutative rings

Elena Bunina
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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 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. 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.

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Elena Bunina. 2023-04-26. Automorphisms of Chevalley groups over commutative rings. https://arxiv.org/abs/2304.13447

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