Central singularities of quantum spaces
type: Item
instance of: scholarly article
title: Central singularities of quantum spaces
zbMATH Open document ID: 0844.17005
published in: Journal of Algebra
publication date: 1996-09-08T00:00:00Z
full work available at URL: 5102.pdf
review text: Let \(A\) be a positively graded connected affine \(\mathbb{C}\)-algebra generated in degree one. Let \(R\) be a central graded subalgebra and assume that \(A\) is a finite module over \(R\). Then \(A\) gives rise to a coherent sheaf \({\mathcal A}\) of algebras over \(Y = \text{Proj} R\); the center \({\mathcal Z}\) of \({\mathcal A}\) (a sheaf of commutative algebras) plays a rôle in the study of Sklyanin algebras at points of finite order. Assume that \(\text{injdim} (A) < \infty\). It is shown in the present paper that the commutative scheme \(\text{Spec} {\mathcal Z}\) has singularities unless the ramification locus of \({\mathcal A}\) is pure of codimension 1. If \(\text{gldim} (A) < \infty\), then the codimension \(\geq 2\) parts of the ramification locus of \({\mathcal A}\) and the singular locus of \(\text{Spec} {\mathcal Z}\) coincide.
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14A05
zbMATH DE Number: 848966
zbMATH Keywords: Sklyanin algebras
zbMATH Keywords: commutative scheme
zbMATH Keywords: singularities
author: Lieven Le Bruyn
reviewed by: Nicolás Andruskiewitsch
MaRDI profile type: Publication
OpenAlex ID: W1974643937
DOI: 10.1006/JABR.1995.1290
description: scientific article; zbMATH DE number 848966