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arXiv · 2510.07059

The isotropy group of a derivation on a Danielewski-type algebra

Abdessamad Ahouita·Rene Baltazar·M'hammed El Kahoui·Sergey Gaifullin
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Abstract

Given an algebraically closed field $k$ of characteristic zero, we consider in this paper $k$-algebras of the form $$A_{c,q}=k[x,y,z]/\big(c(x)z-q(x,y)\big),$$ where $c(x)\in k[x]$ is a polynomial of degree at least two and $q(x,y)\in k[x,y]$ is a quasi-monic polynomial of degree at least two with respect to $y$. We give a complete description of the $k$-automorphism group of $A_{c,q}$ as an abstract group. Moreover, for every non-locally nilpotent $k$-derivation $\delta$ of $A_{c,q}$ we prove that the isotropy group of $\delta$ is a linear algebraic group of dimension at most three.

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Abdessamad Ahouita, Rene Baltazar, M'hammed El Kahoui, Sergey Gaifullin. 2025-10-08. The isotropy group of a derivation on a Danielewski-type algebra. https://arxiv.org/abs/2510.07059

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