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arXiv · 0806.4152

Dimension of automorphisms with fixed degree for polynomial algebras

Vesselin Drensky·Jie-Tai Yu
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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 $\max\{\text{deg}(f),\text{deg}(g)\}=n\geq 2$ 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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Vesselin Drensky, Jie-Tai Yu. 2008-07-07. Dimension of automorphisms with fixed degree for polynomial algebras. https://arxiv.org/abs/0806.4152

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