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

This article is cited in 1 scientific paper (total in 1 paper)

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
Received: 02.03.2015
Revised: 16.03.2015
Language:

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}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Reyes, H. Suarez, “Bases for quantum algebras and skew Poincaré-Birkhoff-Witt extensions”, Momento, 2017, no. 54, 54–75  crossref  isi
  • Algebra and Discrete Mathematics
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