HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS

Abstract

We introduce hom-associative Ore extensions as non-unital, nonassociative

Ore extensions with a hom-associative multiplication, and give

some necessary and sucient conditions when such exist. Within this framework,

we construct families of hom-associative quantum planes, universal enveloping

algebras of a Lie algebra, andWeyl 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.

Keywords

• Hom-associative Ore extensions,hom-associative Weyl algebras

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