English

Elementary equivalence of Chevalley groups over fields

Group Theory 2007-05-23 v1 Logic

Abstract

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

Cite

@article{arxiv.math/0702044,
  title  = {Elementary equivalence of Chevalley groups over fields},
  author = {E. I. Bunina},
  journal= {arXiv preprint arXiv:math/0702044},
  year   = {2007}
}

Comments

55 pages