Let $\rho$ be an algebraic action of the additive group $\mathbb{ C}^+$ on the three-dimensional affine space $\mathbb{ C}^3$. We describe the group $\textrm{ Cent}(\rho)$ of polynomial automorphisms of $\mathbb{ C}^3$ that commute with $\rho$. A particular emphasis lies in the description of the automorphisms in $\textrm{ Cent}(\rho)$ coming from algebraic $\mathbb{ C}^+$-actions. As an application we prove that the automorphisms in $\textrm{ Cent}(\rho)$ that are the identity on the algebraic quotient of $\rho$ form a characteristic subgroup of $\textrm{ Cent}(\rho)$.
Categories: math.AG