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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154757 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| Summary: | 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.
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| ISSN: | 1726-3255 |