Ivan Kaygorodov ; Samuel A. Lopes ; Farukh Mashurov - Actions of the additive group Ga on certain noncommutative deformations of the plane

cm:9543 - Communications in Mathematics, July 15, 2021, Volume 29 (2021), Issue 2 (Special Issue: 3rd International Workshop on Nonassociative Algebras in Málaga) - https://doi.org/10.2478/cm-2021-0024
Actions of the additive group Ga on certain noncommutative deformations of the plane

Authors: Ivan Kaygorodov ; Samuel A. Lopes ; Farukh Mashurov

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 − 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.


Volume: Volume 29 (2021), Issue 2 (Special Issue: 3rd International Workshop on Nonassociative Algebras in Málaga)
Published on: July 15, 2021
Imported on: May 11, 2022
Keywords: [MATH]Mathematics [math]


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