An explicit tame factorization of the four-variable Anick automorphism

Abstract

Let $\delta =xz-yt$. We give an explicit tame factorization of the Anick automorphism $(x+\delta t,y+\delta z,z,t)$ of $F[x,y,z,t]$. After a linear change of coordinates, the factorization consists of sixteen elementary automorphisms, all fixing $z$. The proof uses a commutator construction with variables already present in the algebra. A complete list of the elementary factors is included in Section 5. The explicit polynomial factorization identities are defined over $\ZZ[1/2]$; no conclusion in characteristic $2$ is asserted.