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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| Дата: | 2015 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2015
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/95 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua: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 |
| 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 |
2024-04-12T06:25:30Z |
| last_indexed |
2024-04-12T06:25:30Z |
| _version_ |
1796109224918384640 |