Examples and quantum sections of schematic algebras
type: Item
instance of: scholarly article
title: Examples and quantum sections of schematic algebras
zbMATH Open document ID: 0892.16020
DOI: 10.1016/S0022-4049(96)00065-5
author: Luc Willaert
author: Fred Van Oystaeyen
published in: Journal of Pure and Applied Algebra
publication date: 1998-06-04T00:00:00Z
review text: In an earlier paper, [J. Pure Appl. Algebra 104, No. 1, 109-122 (1995; Zbl 0854.16027)], the authors developed their notion of a ``schematic algebra'', a (non-commutative) connected graded Noetherian \(k\)-algebra having a finite collection \(\{S_i\}\) of Ore sets such that a graded left ideal \(I\) with \(I\cap S_i\neq\emptyset\) for all \(i\) must contain a power of the augmentation ideal. They proposed this concept as providing a notion of scheme in the setting of non-commutative geometry. The purpose of the present paper is to provide examples of schematic algebras -- for example, the Rees rings of almost commutative rings, the coordinate ring of quantum \(2\times 2\) matrices, quantum Weyl algebras and the three dimensional Sklyanin algebra are shown to be schematic.
Mathematics Subject Classification ID: 16U20
Mathematics Subject Classification ID: 14A22
Mathematics Subject Classification ID: 16S80
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16S60
Mathematics Subject Classification ID: 16P50
zbMATH DE Number: 1067516
zbMATH Keywords: connected graded Noetherian algebras
zbMATH Keywords: Ore sets
zbMATH Keywords: schemes
zbMATH Keywords: non-commutative geometry
zbMATH Keywords: schematic algebras
zbMATH Keywords: Rees rings
zbMATH Keywords: quantum Weyl algebras
zbMATH Keywords: Sklyanin algebras
reviewed by: Kenneth A. Brown
MaRDI profile type: Publication
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full work available at URL: s0022-4049(96)00065-5
OpenAlex ID: W1994203945
description: scientific article; zbMATH DE number 1067516