Length four polynomial automorphisms

摘要

We study the structure of length four polynomial automorphisms of R [X, Y] when R is a unique factorization domain. The results from this study are used to prove that, if SL_m (R[X_1 X_2 X_n]) = Em (R[X_1 X_2 X_n]) for all n m ≥ 0, then all length four polynomial automorphisms of R[X,Y] that are commutators are stably tame.