Quantum sections and gauge algebras
type: Item
instance of: scholarly article
title: Quantum sections and gauge algebras
zbMATH Open document ID: 0826.16040
DOI: 10.5565/PUBLMAT_362A92_28
published in: Publicacions Matemàtiques
publication date: 1994-06-09T00:00:00Z
full work available at URL: https://eudml.org/doc/41746
review text: There is an interplay between properties of a filtered ring \(R\) and its associated graded and Rees rings, denoted here \(G(R)\) and \(\widetilde{R}\), respectively. For instance, if \(G(R)\) is a commutative Noetherian domain, one can lift the scheme structure of \(\text{Proj }G(R)\) to \(\text{Proj }\widetilde{R}\) by using quantum sections. The hypothesis on \(G(R)\) can be weakened: For example, one can assume \(G(R)\) to be a non-commutative quadratic Auslander-regular algebra (in this case, \(R\) is called a gauge algebra). The article under review is a survey on these topics, introducing the basic definitions and expanding concrete examples.
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 17A80
Mathematics Subject Classification ID: 16W60
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16U20
Mathematics Subject Classification ID: 16S60
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 203329
zbMATH Keywords: filtered rings
zbMATH Keywords: associated graded rings
zbMATH Keywords: commutative Noetherian domains
zbMATH Keywords: schemes
zbMATH Keywords: quantum sections
zbMATH Keywords: non-commutative quadratic Auslander-regular algebras
zbMATH Keywords: gauge algebras
zbMATH Keywords: survey
zbMATH Keywords: associated Rees rings
author: Lieven Le Bruyn
author: Fred Van Oystaeyen
reviewed by: Nicolás Andruskiewitsch
MaRDI profile type: Publication
OpenAlex ID: W2076434387
description: scientific article; zbMATH DE number 203329