Automorphisms of ℂ³Commuting with a ℂ⁺-Action

Abstract

Abstract. Let ρ be an algebraic action of the additive group C + on the threedimensional affine space C 3 . We describe the group Cent(ρ) of polynomial automorphisms of C 3 that commute with ρ. A particular emphasis lies in the description of the automorphisms in Cent(ρ) coming from algebraic C + -actions. As an application we prove that the automorphisms in Cent(ρ) that are the identity on the algebraic quotient of ρ form a characteristic subgroup of Cent(ρ).