eng
episciences.org
Communications in Mathematics
1804-1388
2336-1298
2021-07-15
Volume 29 (2021), Issue 2...
10.2478/cm-2021-0024
9543
journal article
Actions of the additive group Ga on certain noncommutative deformations of the plane
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.
https://cm.episciences.org/9543/pdf
[MATH]Mathematics [math]