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Mat. Sb., 2019, Volume 210, Number 8, Pages 3–28 (Mi msb9069)  

Isomorphisms and elementary equivalence of Chevalley groups over commutative rings

E. I. Bunina

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: It is proved that two Chevalley groups with indecomposable root systems of rank $>1$ over commutative rings (which contain in addition $1/2$ for the types $\mathbf A_2$, $\mathbf B_l$, $\mathbf C_l$, $\mathbf F_4$, and $\mathbf G_2$, and $1/3$ for the type $\mathbf G_2$) are isomorphic or elementarily equivalent if and only if the corresponding root systems coincide, the weight lattices of the representation of the Lie algebra coincide, and the rings are isomorphic or elementarily equivalent, respectively. The isomorphisms of adjoint (elementary) Chevalley groups over the rings of the above types are also described.
Bibliography: 25 titles.

Keywords: Chevalley groups over commutative rings, automorphisms, isomorphisms, elementary equivalence.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00895-а
This research was supported by the Russian Foundation for Basic Research (grant no. 17-01-00895-a).


DOI: https://doi.org/10.4213/sm9069

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English version:
Sbornik: Mathematics, 2019, 210:8, 1067–1091

Bibliographic databases:

UDC: 512.54.03+512.743.7
MSC: Primary 20G35; Secondary 20G41, 20H25
Received: 20.01.2018 and 30.09.2018

Citation: E. I. Bunina, “Isomorphisms and elementary equivalence of Chevalley groups over commutative rings”, Mat. Sb., 210:8 (2019), 3–28; Sb. Math., 210:8 (2019), 1067–1091

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