Automorphisms of the Lie algebra of vector fields on affine $n$-space

Abstract

We show that every Lie algebra automorphism of the vector fields Vec( A n ) of affine n -space A n , of the vector fields Vec c ( A n ) with constant divergence, and of the vector fields Vec 0 ( A n ) with divergence zero is induced by an automorphism of A n . This generalizes results of the second author obtained in dimension 2, see [Reg13]. The case of Vec( A n ) goes back to Kulikov [Kul92].