Isomorphisms and elementary equivalence of Chevalley groups over commutative rings

E. I. Bunina

doi:10.1070/SM9069

Isomorphisms and elementary equivalence of Chevalley groups over commutative rings

E. I. Bunina

Lomonosov Moscow State University

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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 A2, B_l, C_l, F4, and G2, and 1/3 for the type G2) 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.

Original language	English
Pages (from-to)	1067-1091
Number of pages	25
Journal	Sbornik Mathematics
Volume	210
Issue number	8
DOIs	https://doi.org/10.1070/SM9069
State	Published - Aug 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.

Funding

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

Funders	Funder number
Russian Foundation for Basic Research	17-01-00895-a

Keywords

Automorphisms
Chevalley groups over commutative rings
Elementary equivalence
Isomorphisms

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10.1070/SM9069

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AB - 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 A2, Bl, Cl, F4, and G2, and 1/3 for the type G2) 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.

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Isomorphisms and elementary equivalence of Chevalley groups over commutative rings

Abstract

Bibliographical note

Funding

Keywords

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