Notes on formal deformations of quantum planes and universal enveloping algebras

Abstract

In these notes, we introduce formal hom-associative deformations of the quantum planes and the universal enveloping algebras of the two-dimensional non-abelian Lie algebras. We then show that these deformations induce formal hom-Lie deformations of the corresponding Lie algebras constructed by using the commutator as bracket.

7 pages; Updated reference to Ore's article with correct name, deleted 17A01 MSC class, corrected a minor typo in a proof