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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2015, Volume 20, Issue 1, Pages 1–12 (Mi adm527)

RESEARCH ARTICLE

Universal property of skew $PBW$ extensions

Juan Pablo Acosta, Oswaldo Lezama

Departamento de Matemáticas, Universidad Nacional de Colombia

Abstract: In this paper we prove the universal property of skew $PBW$ extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of non-commutative rings. Skew $PBW$ extensions include as particular examples Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials, diffusion algebras, Manin algebra of quantum matrices, among many others. As a corollary we will give a new short proof of the Poincaré-Birkhoff-Witt theorem about the bases of enveloping algebras of finite-dimensional Lie algebras.

Keywords: skew polynomial rings, skew $PBW$ extensions, $PBW$ bases, quantum algebras.

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Bibliographic databases:
MSC: Primary 16S10, 16S80; Secondary 16S30, 16S36
Revised: 16.03.2015
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Citation: Juan Pablo Acosta, Oswaldo Lezama, “Universal property of skew $PBW$ extensions”, Algebra Discrete Math., 20:1 (2015), 1–12

Citation in format AMSBIB
\Bibitem{AcoLez15} \by Juan~Pablo~Acosta, Oswaldo~Lezama \paper Universal property of skew $PBW$ extensions \jour Algebra Discrete Math. \yr 2015 \vol 20 \issue 1 \pages 1--12 \mathnet{http://mi.mathnet.ru/adm527} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3431947} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000378728700002}