Chein Automorphisms of Free Metabelian Anticommutative Algebras

Abstract

We describe all automorphisms of a free metabelian anticommutative algebra of rank $n\geq 3$ over a field $K$ that move only one variable while fixing the others. Such automorphisms are called Chein automorphisms in the cases of free metabelian groups and free metabelian Lie algebras. We show that all automorphisms of a free metabelian anticommutative algebra of rank $n=2$ are linear, and that the simplest non elementary Chein automorphism of degree $3$ is absolutely wild for all $n\geq 3$.