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

Abstract

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].