Dimension of automorphisms with fixed degree for polynomial algebras

Abstract

Let $K[x,y]$ be the polynomial algebra in two variables over an algebraically closed field $K$. We generalize to the case of any characteristic the result of Furter that over a field of characteristic zero the set of automorphisms $(f,g)$ of $K[x,y]$ such that $\max \{\text{deg}(f),\text{deg}(g)\}=n\ge 2$ is constructible with dimension $n+6$. The same result holds for the automorphisms of the free associative algebra $K<x,y>$. We have also obtained analogues for free algebras with two generators in Nielsen -- Schreier varieties of algebras.

10 pages

References in corpus (1)

• Automorphisms of polynomial algebras and Dirichlet series