Pascal finite polynomial automorphisms

Abstract

The class of Pascal finite polynomial automorphisms is a subclass of the class of locally finite ones allowing a more effective approach. In characteristic zero, a Pascal finite automorphism is the exponential map of a locally nilpotent derivation. However, Pascal finite automorphisms are defined in any characteristic, and therefore constitute a generalization of exponential automorphisms to positive characteristic. In this paper, we prove several properties of Pascal finite automorphisms. We obtain in particular that the Pascal finite property is stable under taking powers but not under composition. This leads us to formulate a generalization of the exponential generators conjecture to arbitrary characteristic.