TRIANGULABILITY CRITERIA FOR ADDITIVE GROUP-ACTIONS ON AFFINE SPACE

This paper concerns algebraic one-parameter subgroups of GA(n)(k), the group of k-algebra automorphisms of the polynomial ring in n variable s over a field k: R(n) = k[X(1),...,X(n)]. These subgroups are of the form exp(tD) (t is an element of k), where D is a locally nilpotent de rivation of R(n). The rank of D is defined; this reduces to the usual notion of rank when D is a linear derivation. A characterization is gi ven of all rank 1 derivations. In addition, the rank of D is used to g ive two criteria for the triangulability of certain actions induced by D (Propositions 2 and 3). These criteria are used to show the existen ce of tame non-triangulable actions in dimension 4 or greater.