Hom-associative Ore extensions and weak unitalizations

Abstract

We introduce hom-associative Ore extensions as non-unital, non-associative 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 hom-associative algebra into a multiplicative, weakly unital hom-associative algebra, which we call a weak unitalization.

17 pages; more material added, including two more examples and a section on weak unitalizations; minor changes made

Cited by in corpus (12)

• Gauge theories on quantum spaces
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
• On the hom-associative Weyl algebras
• Hilbert's basis theorem for non-associative and hom-associative Ore extensions
• Notes on formal deformations of quantum planes and universal enveloping algebras
• Ideals in hom-associative Weyl algebras
• Multi-parameter formal deformations of ternary hom-Nambu-Lie algebras
• Ore Extensions of Abelian Groups with Operators
• The hom-associative Weyl algebras in prime characteristic
• The higher-order hom-associative Weyl algebras
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects