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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2015 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2015
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| Zitieren: | 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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Acosta, J,.P. Lezama, O. 2019-06-15T20:00:54Z 2019-06-15T20:00:54Z 2015 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. https://nasplib.isofts.kiev.ua/handle/123456789/154757 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Universal property of skew PBW extensions Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Universal property of skew PBW extensions |
| spellingShingle |
Universal property of skew PBW extensions Acosta, J,.P. Lezama, O. |
| 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 |
| author |
Acosta, J,.P. Lezama, O. |
| author_facet |
Acosta, J,.P. Lezama, O. |
| publishDate |
2015 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.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. |
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AT acostajp universalpropertyofskewpbwextensions AT lezamao universalpropertyofskewpbwextensions |
| first_indexed |
2025-12-02T11:38:04Z |
| last_indexed |
2025-12-02T11:38:04Z |
| _version_ |
1850862376863137792 |