Homogeneization of locally nilpotent derivations and an application to \(k[X,Y,Z]\) (Q1770539)

The author considers locally nilpotent derivations \(D\) of a graded \(k\)-algebra \(B\), where \(k\) is a field of characteristic zero. Since \(B\) is graded, there is an associated homogeneous derivation gr\((D)\) of \(B\), and the author's strategy is to study \(D\) via gr\((D)\). He succeeds in giving several nice results in this direction, with special emphasis on the case \(B=k[x,y,z]\), a polynomial ring in three variables. One notable result is proposition 4.6, which asserts that if \(D^2x=D^2y=D^2z=0\), then \(D\) is conjugate to \(f(x,y)\partial /\partial z\) for some \(f\). The paper is an outgrowth of the author's thesis.