{"docId":9543,"paperId":9543,"url":"https:\/\/cm.episciences.org\/9543","doi":"10.2478\/cm-2021-0024","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":648,"name":"Volume 29 (2021), Issue 2 (Special Issue: 3rd International Workshop on Nonassociative Algebras in M\u00e1laga)"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-03665021","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-03665021v1","dateSubmitted":"2022-05-11 15:42:52","dateAccepted":null,"datePublished":"2021-07-15 00:00:00","titles":{"en":"Actions of the additive group Ga on certain noncommutative deformations of the plane"},"authors":["Kaygorodov, Ivan","Lopes, Samuel A.","Mashurov, Farukh"],"abstracts":{"en":"We connect the theorems of Rentschler [18] and Dixmier [10] onlocally nilpotent derivations and automorphisms of the polynomial ring A0and of the Weyl algebra A1, both over a field of characteristic zero, byestablishing the same type of results for the family of algebrasAh = hx, y | yx \u2212 xy = h(x)i,where h is an arbitrary polynomial in x. In the second part of the paper weconsider a field F of prime characteristic and study F[t]-comodule algebrastructures on Ah. We also compute the Makar-Limanov invariant of absolute constants of Ah over a field of arbitrary characteristic and show howthis subalgebra determines the automorphism group of Ah."},"keywords":["[MATH]Mathematics [math]"]}