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 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154757 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Universal property of skew PBW extensions / J,.P. Acosta, O. Lezama // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 1. — С. 1-12 . — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-154757 |
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dspace |
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irk-123456789-1547572019-06-16T01:29:07Z Universal property of skew PBW extensions Acosta, J,.P. Lezama, O. 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. 2015 Article Universal property of skew PBW extensions / J,.P. Acosta, O. Lezama // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 1. — С. 1-12 . — Бібліогр.: 10 назв. — англ. 1726-3255 2010 MSC:Primary: 16S10, 16S80; Secondary: 16S30, 16S36. http://dspace.nbuv.gov.ua/handle/123456789/154757 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Acosta, J,.P. Lezama, O. |
| spellingShingle |
Acosta, J,.P. Lezama, O. Universal property of skew PBW extensions Algebra and Discrete Mathematics |
| author_facet |
Acosta, J,.P. Lezama, O. |
| author_sort |
Acosta, J,.P. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154757 |
| citation_txt |
Universal property of skew PBW extensions / J,.P. Acosta, O. Lezama // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 1. — С. 1-12 . — Бібліогр.: 10 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT acostajp universalpropertyofskewpbwextensions AT lezamao universalpropertyofskewpbwextensions |
| first_indexed |
2023-05-20T17:44:13Z |
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2023-05-20T17:44:13Z |
| _version_ |
1796153972003700736 |