Elementary equivalence of Chevalley groups over fields

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Abstract

It is proved that (elementary) Chevalley groups Gπ (Φ, K) and Gπ′ (Φ′, K′) (or Eπ (Φ, K) and Eπ′ (Φ′, K′)) over infinite fields K and K′ of characteristic different from 2, with weight lattices Λ and Λ′, respectively, are elementarily equivalent if and only if the root systems Φ and Φ′ are isomorphic, the fields K and K′ are elementarily equivalent, and the lattices Λ and Λ′ coincide.

Original languageEnglish
Pages (from-to)155-190
Number of pages36
JournalJournal of Mathematical Sciences
Volume152
Issue number2
DOIs
StatePublished - Jul 2008
Externally publishedYes

Bibliographical note

Funding Information:
This work was partially supported by the President of the Russian Federation grant MK-904.2006.1 and by the Russian Foundation for Basic Research grant 05-01-01048.

Funding

This work was partially supported by the President of the Russian Federation grant MK-904.2006.1 and by the Russian Foundation for Basic Research grant 05-01-01048.

FundersFunder number
Russian Foundation for Basic Research05-01-01048
Council on grants of the President of the Russian FederationMK-904.2006.1

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