  In this paper we consider the very wide class of varieties of representations
of Lie algebras over the field k, which has characteristic 0. We study the
relation between the geometric equivalence and automorphic equivalence of the
representations of these varieties. We calculate the group, which measures the
difference between the geometric equivalence and automorphic equivalence of
representations of theses varieties. In Section 5, we present one example of
the subvariety of the variety of all the representations of the Lie algebras
over the field k, and two representations from these variety which are
automorphically equivalent but not geometrically equivalent.
