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Article Dans Une Revue Communications in Mathematics Année : 2021

Actions of the additive group Ga on certain noncommutative deformations of the plane

Résumé

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 Ah = hx, y | yx − xy = h(x)i, 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.
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hal-03665021 , version 1 (11-05-2022)

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Ivan Kaygorodov, Samuel A. Lopes, Farukh Mashurov. Actions of the additive group Ga on certain noncommutative deformations of the plane. Communications in Mathematics, 2021, Volume 29 (2021), Issue 2 (Special Issue: 3rd International Workshop on Nonassociative Algebras in Málaga) (2), pp.269 - 279. ⟨10.2478/cm-2021-0024⟩. ⟨hal-03665021⟩
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