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arXiv · 1710.04190

Hom-associative Ore extensions and weak unitalizations

Per Bäck·Johan Richter·Sergei Silvestrov
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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.

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Per Bäck, Johan Richter, Sergei Silvestrov. 2017-10-11. Hom-associative Ore extensions and weak unitalizations. https://doi.org/10.24330/ieja.440245

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