Actions of the additive group G<inf>a</inf>on certain noncommutative deformations of the plane

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Kaygorodov I. (Author) Other; Samuel A Lopes (Author) FCUP; Mashurov F. (Author) Other

Journal

Title: Communications in Mathematics

Vol. 29

Pages: 269-279

ISSN: 1804-1388

Indexing

Scopus - 1 Citation

Other information

Authenticus ID: P-00W-0WZ

DOI: 10.2478/cm-2021-0024

Abstract (EN): We connect the theorems of Rentschler [18] and Dixmier [10] on locally nilpotent derivations and automorphisms of the polynomial ring A0 and of the Weyl algebra A1, both over a field of characteristic zero, by establishing the same type of results for the family of algebras {equation presented} where h is an arbitrary polynomial in x. In the second part of the paper we consider a field F of prime characteristic and study F[t]-comodule algebra structures on Ah. We also compute the Makar-Limanov invariant of absolute constants of Ah over a field of arbitrary characteristic and show how this subalgebra determines the automorphism group of Ah.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10