Submission date: 29 August 2022

Abstract:

In this paper we prove that if G(R)=G_π (Φ,R) (E(R)=E_π(Φ, R)) is an (elementary) Chevalley group of rank > 1, R is a local ring (with 1/2 for the root systems A_2, B_l, C_l, F_4, G_2 and with 1/3 for G_{2}), then the group G(R) (or (E(R)) is regularly bi-interpretable with the ring R. As a consequence of this theorem, we show that the class of all Chevalley groups over local rings (with the listed restrictions) is elementary definable, i.e., if for an arbitrary group H we have H ≡ G_π(Φ, R), than there exists a ring R' ≡ R such that H ≅ G_π(Φ,R').

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Full text arXiv 2208.13623: pdf, ps.