Elementary equivalence of Chevalley groups over fields

Details Elementary equivalence of Chevalley groups over fields Elementary equivalence of Chevalley groups over fields

2007-02-02

arxiv.org/abs/math/0702044v1

Fundamentalnaya i Prikladnaya Matematika, 2006, 12(8), 29-77 (in Russian)

Mathematics

Group Theory

55 pages

Scientific paper

It is proved that (elementary) Chevalley groups $G_\pi (\Phi,K)$ and $G_{\pi'}(\Phi',K')$ (or $E_\pi (\Phi,K)$ and $E_{\pi'}(\Phi',K'))$ over infinite fields $K$ and $K'$ of characteristics $\ne 2$, with weight lattices $\Lambda$ and $\Lambda'$, respectively, are elementarily equivalent if and only if the root systems $\Phi$ and $\Phi'$ are isomorphic, the fields $K$ and $K'$ are elementarily equivalent, the lattices $\Lambda$ and $\Lambda'$ coincide.

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