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Algebra and Discrete Mathematics, 2015, Volume 20, Issue 1, Pages 1–12
(Mi adm527)
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This article is cited in 5 scientific papers (total in 5 papers)
RESEARCH ARTICLE
Universal property of skew $PBW$ extensions
Juan Pablo Acosta, Oswaldo Lezama Departamento de Matemáticas, Universidad Nacional de Colombia
Abstract:
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 Poincaré-Birkhoff-Witt theorem about the bases of enveloping algebras of finite-dimensional Lie algebras.
Keywords:
skew polynomial rings, skew $PBW$ extensions, $PBW$ bases, quantum algebras.
Received: 02.03.2015 Revised: 16.03.2015
Citation:
Juan Pablo Acosta, Oswaldo Lezama, “Universal property of skew $PBW$ extensions”, Algebra Discrete Math., 20:1 (2015), 1–12
Linking options:
https://www.mathnet.ru/eng/adm527 https://www.mathnet.ru/eng/adm/v20/i1/p1
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Abstract page: | 291 | Full-text PDF : | 64 | References: | 42 |
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