Geodesic
Actions of the additive group $ {G}_a$ on certain noncommutative deformations of the plane
Communications in Mathematics, Tome 29 (2021) no. 2, pp. 269-279.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $A _h$.
Classification : 13N15, 16S10, 16S32, 16W20
Keywords: Derivations; iterative higher derivations; rings of differential operators; Weyl algebra 
@article{COMIM_2021__29_2_a8,
     author = {Kaygorodov, Ivan and Lopes, Samuel A. and Mashurov, Farukh},
     title = {Actions of the additive group $ {G}_a$ on certain noncommutative deformations of the plane},
     journal = {Communications in Mathematics},
     pages = {269--279},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2021},
     mrnumber = {4285757},
     zbl = {07426423},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2021__29_2_a8/}
}
TY  - JOUR
AU  - Kaygorodov, Ivan
AU  - Lopes, Samuel A.
AU  - Mashurov, Farukh
TI  - Actions of the additive group $ {G}_a$ on certain noncommutative deformations of the plane
JO  - Communications in Mathematics
PY  - 2021
SP  - 269
EP  - 279
VL  - 29
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/COMIM_2021__29_2_a8/
LA  - en
ID  - COMIM_2021__29_2_a8
ER  - 
%0 Journal Article
%A Kaygorodov, Ivan
%A Lopes, Samuel A.
%A Mashurov, Farukh
%T Actions of the additive group $ {G}_a$ on certain noncommutative deformations of the plane
%J Communications in Mathematics
%D 2021
%P 269-279
%V 29
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/COMIM_2021__29_2_a8/
%G en
%F COMIM_2021__29_2_a8
Kaygorodov, Ivan; Lopes, Samuel A.; Mashurov, Farukh. Actions of the additive group $ {G}_a$ on certain noncommutative deformations of the plane. Communications in Mathematics, Tome 29 (2021) no. 2, pp. 269-279. http://geodesic.mathdoc.fr/item/COMIM_2021__29_2_a8/