Isomorphisms and elementary equivalence of Chevalley groups over commutative rings

E. I. Bunina

Sbornik. Mathematics, Tome 210 (2019) no. 8, pp. 1067-1091

Résumé

It is proved that two Chevalley groups with indecomposable root systems of rank $>1$ over commutative rings (which contain in addition $1/2$ for the types $\mathbf A_2$, $\mathbf B_l$, $\mathbf C_l$, $\mathbf F_4$, and $\mathbf G_2$, and $1/3$ for the type $\mathbf G_2$) are isomorphic or elementarily equivalent if and only if the corresponding root systems coincide, the weight lattices of the representation of the Lie algebra coincide, and the rings are isomorphic or elementarily equivalent, respectively. The isomorphisms of adjoint (elementary) Chevalley groups over the rings of the above types are also described. Bibliography: 25 titles.

Détail

Keywords: Chevalley groups over commutative rings, automorphisms, isomorphisms, elementary equivalence.

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