HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS

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International Electronic Journal of Algebra
Volume:24 Issue:24
HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS

HOM-ASSOCIATIVE ORE EXTENSIONS AND WEAK UNITALIZATIONS

Authors : Per BACK, Johan RİCHTER, Sergei SİLVESTROV

Pages : 174-194

Doi:10.24330/ieja.440245

View : 8 | Download : 9

Publication Date : 2018-07-05

Article Type : Research Paper

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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