| Title:
|
Actions of the additive group $ {G}_a$ on certain noncommutative deformations of the plane (English) |
| Author:
|
Kaygorodov, Ivan |
| Author:
|
Lopes, Samuel A. |
| Author:
|
Mashurov, Farukh |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
29 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
269-279 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We connect the theorems of Rentschler \cite {rR68} and Dixmier \cite {jD68} on locally nilpotent derivations and automorphisms of the polynomial ring $A _0$ and of the Weyl algebra $A _1$, both over a field of characteristic zero, by establishing the same type of results for the family of algebras $$A _h=\langle x, y\mid yx-xy=h(x)\rangle \,,$$ where $h$ is an arbitrary polynomial in $x$. In the second part of the paper we consider a field $\mathbb{F}$ of prime characteristic and study $\mathbb{F}[t]$\HH comodule algebra structures on $A _h$. We also compute the Makar-Limanov invariant of absolute constants of $A _h$ over a field of arbitrary characteristic and show how this subalgebra determines the automorphism group of $A _h$. (English) |
| Keyword:
|
Derivations |
| Keyword:
|
iterative higher derivations |
| Keyword:
|
rings of differential operators |
| Keyword:
|
Weyl algebra |
| MSC:
|
13N15 |
| MSC:
|
16S10 |
| MSC:
|
16S32 |
| MSC:
|
16W20 |
| idZBL:
|
Zbl 07426423 |
| idMR:
|
MR4285757 |
| . |
| Date available:
|
2021-11-04T12:27:31Z |
| Last updated:
|
2021-12-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149194 |
| . |
| Reference:
|
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