Generalization of a counterexample to Derksen’s theorem in characteristic two

Abstract

The Derksen group is the subgroup of the tame subgroup which is generated by affine automorphisms and one particular non-linear automorphism. It is known that the Derksen group is equal to the entire tame subgroup in characteristic zero and in dimension greater than or equal to three (Derksen's Theorem). Recently, Maubach and Willems (Serdica Math J 37:305-322, 2011) proved that if the defining field of polynomial automorphisms is prime field of characteristic two, then Derksen's Theorem does not hold in dimension three. In this paper, we generalize the above counterexample to the case of higher dimension.