Locally nilpotent derivations of affine domains
Any locally nilpotent derivation of an affine domain is equivalent to a restriction of a Jacobian type derivation of a polynomial ring.
AK-invariant of affine domains
The AK-invariant of an affine domain is the intersection of kernels of locally nilpotent derivations on this domain. It allows often to distinguish exotic structures from Euclidean spaces, especially in dimension 3. In this paper we develop methodology for computation of AK-invariant and give examples of its applications. 2000 Mathematics Subject Classification: 1405, 14R10, 14R20.
Locally Nilpotent Derivations over a UFD and an Application to Rank Two Locally Nilpotent Derivations ofk[X1,…,Xn]☆
Abstract Given a UFD R containing the rational numbers, we study locally nilpotent R -derivations of the polynomial ring R [ X ,  Y ]; in particular, we give a generalization of Rentschler's Theorem and a criterion for the existence of a slice. These results are then applied to describe rank two locally nilpotent derivations of k [ X 1 ,…, X n ], where k is a field of characteristic zero. We also give an example of a nontriangulable locally nilpotent derivation of k [ X ,  Y ,  Z ] whose set of fixed points is a line.