New stably tame automorphisms of polynomial algebras

Let K[X, Y] = K[x(1),..., x(n), y(1),..., y(m)] be the polynomial algebra i n m + n variables over a field K of characteristic 0. Let delta be a locall y nilpotent derivation of K[X, Y] such that delta(y(i)) = 0, i = 1,..., m, and let delta act as a K[Y]-affine transformation over the free K[Y]-module freely generated by x(1),..., x(n). We prove that the automorphism exp(w d elta) of K[X, Y] is stably tame for every polynomial w from the kernel ker( delta) of delta. This result is applied to the automorphisms of the polynom ial algebra in five variables introduced recently by Drensky and Gupta and arising from wild automorphisms of generic matrix algebras. We also give an algorithm for constructing new stably tame automorphisms in any number of variables and, hence, new potential candidates for wild automorphisms. (C) 2000 Academic Press.