Global homological dimension of multifiltered rings and quantized enveloping algebras
type: Item
instance of: scholarly article
title: Global homological dimension of multifiltered rings and quantized enveloping algebras
zbMATH Open document ID: 0945.16011
author: F. J. Lobillo
author: José Gómez-Torrecillas
published in: Journal of Algebra
publication date: 2000-07-05T00:00:00Z
review text: The authors consider multifiltered rings (by the free Abelian semigroup \(\mathbb{N}^p\) with a certain admissible order), the associated graded ring and the transfer of certain properties from one to the other. The connection between multifiltered and graded modules is specialized to free and projective modules. As a consequence it is proved that the projective dimension of a multifiltered module is bounded by the projective dimension of the associated graded module. Similar bounds are given for Krull and flat dimensions. The results are applied to several quantum groups.
reviewed by: Constantin Năstăsescu
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16W70
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16P60
zbMATH DE Number: 1429457
zbMATH Keywords: multifiltered rings
zbMATH Keywords: graded rings
zbMATH Keywords: graded modules
zbMATH Keywords: projective dimensions
zbMATH Keywords: flat dimensions
zbMATH Keywords: Krull dimensions
zbMATH Keywords: quantum groups
MaRDI profile type: Publication
full work available at URL: jabr.1999.8101
OpenAlex ID: W2132395169
cites work: Quantum deformations of GLn
cites work: Q4693774
cites work: Q4395581
cites work: Q4280747
cites work: Gelfand-Kirillov dimension of multi-filtered algebras
cites work: A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
cites work: A simple localization of the quantized Weyl algebra
cites work: Quantum groups at roots of 1
cites work: Q3786586
cites work: Q3957087
cites work: PBW-bases of quantum groups.
cites work: A note on filtered rings
cites work: Ideals in universal enveloping algebras of solvable lie algebras
DOI: 10.1006/JABR.1999.8101
description: scientific article; zbMATH DE number 1429457