Universal property of skew PBW extensions

Juan Pablo Acosta, Oswaldo Lezama

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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 languageEnglish
Pages (from-to)1-12
Number of pages12
JournalAlgebra and Discrete Mathematics
Volume20
Issue number1
StatePublished - 1 Jan 2015
Externally publishedYes

Keywords

  • PBW bases
  • Quantum algebras
  • Skew PBW extensions
  • Skew polynomial rings

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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