Elementary equivalence of Chevalley groups over fields

E. I. Bunina

Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 8, pp. 29-77.

Résumé

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 characteristic different from 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, and the lattices $\Lambda$ and $\Lambda'$ coincide.

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