Isomorphisms and elementary equivalence of Chevalley groups over commutative rings

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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, 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.

Original languageEnglish
Pages (from-to)1067-1091
Number of pages25
JournalSbornik Mathematics
Volume210
Issue number8
DOIs
StatePublished - Aug 2019
Externally publishedYes

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).

FundersFunder number
Russian Foundation for Basic Research17-01-00895-a

    Keywords

    • Automorphisms
    • Chevalley groups over commutative rings
    • Elementary equivalence
    • Isomorphisms

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