The quantum Poincaré-Birkhoff-Witt theorem
type: Item
instance of: scholarly article
title: The quantum Poincaré-Birkhoff-Witt theorem
zbMATH Open document ID: 0755.17006
DOI: 10.1007/BF02099007
author: Roland Berger
published in: Communications in Mathematical Physics
publication date: 1992-09-26T00:00:00Z
review text: Ce travail est consacré à l'étude d'algèbres associatives non commutatives, dont le défault de commutativité dépend de paramètres noté \(q_{ij}\): ce sont les \(q\)-algèbres, dont des exemples sont les algèbres \(q\)-enveloppantes que l'on rencontre dans la théorie algébrique des groupes quantiques. L'auteur donne des conditions portant sur les relations définissant l'algèbre pour que l'algèbre admette la même base que l'algèbre des polynômes, ou encore soit une déformation non commutative de l'algèbre des polynômes. L'exemple de l'algèbre de Drinfeld associée à \({\mathfrak{sl}}(2)\) est ensuite développé en détails.
reviewed by: Claude Roger
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 54711
zbMATH Keywords: quantum groups
zbMATH Keywords: deformation
zbMATH Keywords: quantization
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02099007
OpenAlex ID: W2045567093
description: scientific article; zbMATH DE number 54711