The group of automorphisms of the Lie algebra of derivations of a polynomial algebra

A short proof is given of Rudakov’s result (announced in A. N. Rudakov, Subalgebras and automorphisms of Lie algebras of Cartan type, Funktsional. Anal. i Prilozhen. 20(1) (1986) 83–84), that the group of automorphisms of the Lie algebra Formula: see text of derivations of a polynomial algebra Formula: see text, over a field of characteristic zero is canonically isomorphic to the group of automorphisms of the polynomial algebra Formula: see text.