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.
Original language | English |
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Pages (from-to) | 1-12 |
Number of pages | 12 |
Journal | Algebra and Discrete Mathematics |
Volume | 20 |
Issue number | 1 |
State | Published - 1 Jan 2015 |
Externally published | Yes |
Keywords
- PBW bases
- Quantum algebras
- Skew PBW extensions
- Skew polynomial rings
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics