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.
Cite
@article{arxiv.1710.04190,
title = {Hom-associative Ore extensions and weak unitalizations},
author = {Per Bäck and Johan Richter and Sergei Silvestrov},
journal= {arXiv preprint arXiv:1710.04190},
year = {2020}
}
Comments
17 pages; more material added, including two more examples and a section on weak unitalizations; minor changes made