Centralizers of locally nilpotent derivations

Abstract

Locally nilpotent derivations of the polynomial ring in n variables over the complex field, algebraic actions of the additive group G a of complex numbers on C n, and vector fields on C n admitting a strictly polynomial flow, are equivalent objects. The polynomial centralizer of the vector field corresponding to a triangulable locally nilpotent derivation is investigated, yielding a triangulability criterion. Several new examples of nontriangulable G a actions on C n are presented.