Locally nilpotent derivations and their applications, III Original Research Article

We give an algorithm to decide if certain derivations are locally nilpotent. This algorithm is used to give a solution of the extendability problem for n≤3 (i.e. canF1, …, Fn−1 be extended to a polynomial automorphism (image) and to indicate a strategy for solving the n-dimensional extendability problem. We also reformulate the cancellation problem in terms of locally nilpotent derivations.