A Poincaré-Birkhoff-Witt theorem for the quantum group of type \(A_ n\)
type: Item
instance of: scholarly article
title: A Poincaré-Birkhoff-Witt theorem for the quantum group of type \(A_ n\)
zbMATH Open document ID: 0677.17011
author: Hiroyuki Yamane
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pja/1195513062
review text: The author describes a linear basis for the \(q\)-analogue \(U_ q(G)\) of the universal enveloping algebra in case \(G={\mathfrak sl}_{N+1}({\mathbb C})\). It follows, that \(U_ q({\mathfrak sl}_{N+1}({\mathbb C}))\) is a left (right) Noetherian ring without zero divisors provided \(q(q^ 8-1)\neq 0\).
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 81Q99
zbMATH DE Number: 4108965
zbMATH Keywords: quantum groups
zbMATH Keywords: \(q\)-deformation of enveloping algebras
zbMATH Keywords: Hopf algebra
zbMATH Keywords: explicit linear basis
zbMATH Keywords: analogue of Poincaré-Birkhoff-Witt theorem
zbMATH Keywords: triangular decomposition
reviewed by: Helmut Boseck
MaRDI profile type: Publication
OpenAlex ID: W2016284972
cites work: Q3715293
cites work: A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
cites work: Infinite dimensional Lie algebras. An introduction
cites work: Quantum deformations of certain simple modules over enveloping algebras
cites work: Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
DOI: 10.3792/PJAA.64.385
description: scientific article; zbMATH DE number 4108965