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JOURNALS // Fundamentalnaya i Prikladnaya Matematika // Archive

Fundam. Prikl. Mat., 2006 Volume 12, Issue 8, Pages 29–77 (Mi fpm28)

This article is cited in 10 papers

Elementary equivalence of Chevalley groups over fields

E. I. Bunina

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 512.54+510.67


 English version:
Journal of Mathematical Sciences (New York), 2008, 152:2, 155–190

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