Dimension of automorphisms with fixed degree for polynomial algebras

Details Dimension of automorphisms with fixed degree for polynomial algebras Dimension of automorphisms with fixed degree for polynomial algebras

2008-06-25

arxiv.org/abs/0806.4152v2

Mathematics

Algebraic Geometry

10 pages

Scientific paper

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 $\max\{\text{deg}(f),\text{deg}(g)\}=n\geq 2$ 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.

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