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We prove that the group of automorphisms of the Lie algebra Der K (Qn ) of derivations of the field of rational functions Qn = K(x 1, . . ., xn ) over a field of characteristic zero is canonically isomorphic to the group of automorphisms of the K-algebra Qn .

THE GROUP OF AUTOMORPHISMS OF THE LIE ALGEBRA OF DERIVATIONS OF A FIELD OF RATIONAL FUNCTIONS