Isomorphisms and elementary equivalence of Chevalley groups over commutative rings

Abstract

It is proved that two Chevalley groups with indecomposable root systems of rank over commutative rings (which contain in addition for the types , , , , and , and for the type ) 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.