Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.07059 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915545605996544 |
|---|---|
| author | Ahouita, Abdessamad Baltazar, Rene Kahoui, M'hammed El Gaifullin, Sergey |
| author_facet | Ahouita, Abdessamad Baltazar, Rene Kahoui, M'hammed El Gaifullin, Sergey |
| contents | 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 $δ$ of $A_{c,q}$ we prove that the isotropy group of $δ$ is a linear algebraic group of dimension at most three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07059 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The isotropy group of a derivation on a Danielewski-type algebra Ahouita, Abdessamad Baltazar, Rene Kahoui, M'hammed El Gaifullin, Sergey Rings and Algebras Algebraic Geometry 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 $δ$ of $A_{c,q}$ we prove that the isotropy group of $δ$ is a linear algebraic group of dimension at most three. |
| title | The isotropy group of a derivation on a Danielewski-type algebra |
| topic | Rings and Algebras Algebraic Geometry |
| url | https://arxiv.org/abs/2510.07059 |