Universal property of skew PBW extensions

Universal property of skew PBW extensions

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 examp...

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Bibliographic Details
Date:2015
Main Authors: Acosta, Juan Pablo, Lezama, Oswaldo
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2015
Subjects:
skew polynomial rings
skew $PBW$ extensions
$PBW$ bases
quantum algebras
Primary: 16S10
16S80; Secondary: 16S30
16S36
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/95
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-95
record_format ojs
spelling admjournalluguniveduua-article-952015-11-10T19:25:54Z Universal property of skew PBW extensions Acosta, Juan Pablo Lezama, Oswaldo skew polynomial rings, skew $PBW$ extensions, $PBW$ bases, quantum algebras Primary: 16S10, 16S80; Secondary: 16S30, 16S36 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 Poincar\'{e}-Birkhoff-Witt theorem about the bases of enveloping algebras of finite-dimensional Lie algebras. Lugansk National Taras Shevchenko University 2015-11-09 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/95 Algebra and Discrete Mathematics; Vol 20, No 1 (2015): A special issue 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/95/pdf Copyright (c) 2015 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2015-11-10T19:25:54Z
collection OJS
language English
topic skew polynomial rings
skew $PBW$ extensions
$PBW$ bases
quantum algebras
Primary: 16S10
16S80; Secondary: 16S30
16S36
spellingShingle skew polynomial rings
skew $PBW$ extensions
$PBW$ bases
quantum algebras
Primary: 16S10
16S80; Secondary: 16S30
16S36
Acosta, Juan Pablo
Lezama, Oswaldo
Universal property of skew PBW extensions
topic_facet skew polynomial rings
skew $PBW$ extensions
$PBW$ bases
quantum algebras
Primary: 16S10
16S80; Secondary: 16S30
16S36
format Article
author Acosta, Juan Pablo
Lezama, Oswaldo
author_facet Acosta, Juan Pablo
Lezama, Oswaldo
author_sort Acosta, Juan Pablo
title Universal property of skew PBW extensions
title_short Universal property of skew PBW extensions
title_full Universal property of skew PBW extensions
title_fullStr Universal property of skew PBW extensions
title_full_unstemmed Universal property of skew PBW extensions
title_sort universal property of skew pbw extensions
description 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 Poincar\'{e}-Birkhoff-Witt theorem about the bases of enveloping algebras of finite-dimensional Lie algebras.
publisher Lugansk National Taras Shevchenko University
publishDate 2015
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/95
work_keys_str_mv AT acostajuanpablo universalpropertyofskewpbwextensions
AT lezamaoswaldo universalpropertyofskewpbwextensions
first_indexed 2025-12-02T15:37:46Z
last_indexed 2025-12-02T15:37:46Z
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