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arXiv · 1412.5193

Universal property of skew $PBW$ extensions

Juan Pablo Acosta López·Oswaldo Lezama
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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.

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Juan Pablo Acosta López, Oswaldo Lezama. 2014-12-16. Universal property of skew $PBW$ extensions. https://arxiv.org/abs/1412.5193

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