HOM-ASSOCIATIVE ORE EXTENSIONS an‎d WEAK UNITALIZATIONS

We introduce hom-associative Ore extensions as non-unital, nonassociative Ore extensions with a hom-associative multiplication, and give some necessary and sufficient conditions when such exist. Within this framework, we construct families of hom-associative quantum planes, universal enveloping algebras of a Lie algebra, and Weyl algebras, all being hom-associative generalizations of their classical counterparts, as well as prove that the latter are simple. We also provide a way of embedding any multiplicative homassociative algebra into a multiplicative, weakly unital hom-associative algebra, which we call a weak unitalization.