0. In his book [1] C. Chevalley defined the replicas for any elements of Lie algebras of algebraic groups of matrices which are defined over fields of characteristic 0, and he characterized algebraic subalgebras as those subalgebras of the general linear algebras which are closed with respect to "replica operation" i. e. those which contain all replicas of any elements of themselves. In this paper we shall define the replica in the case of any algebraic groups defined over fields of characterestic 0 and show that the same characterization of algebraic subalgebras is true in this case too.1. Let G be a connected algebraic group 0

In the section 1 we give a Galois correspondence between a family of subfields of the function field of a connected algebraic group G and a family of algebraic subgroups of G. Generally, if the universal domain is of characteristic p > 0, any algebraic subalgebras of the Lie algebras of algebraic groups are />-algebras, but the converse is not true. In the section 2 we give a necessary and sufficient condition for />-subalgebra of the Lie algebra Q of G to be algebraic, and we show that a subalgebra is a />-subalgebra if and only if it is replica closed. If G is affine, the ^-subalgebra generated by one element of g is not only replica closed but algebraic. We treat />-subalgebras generated by one element in the section 3. In the section 4 we give some examples showing that />-subalgebras of Q are not generally algebraic and that the global analogy of the characterization of algebraic subalgebras does not hold even if the universal domain is of characteristic 0.

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