An example of Bernstein duality
type: Item
instance of: scholarly article
title: An example of Bernstein duality
zbMATH Open document ID: 0962.16008
published in: Advances in Mathematics
publication date: 2001-03-19T00:00:00Z
review text: The authors show a local duality on \(K\)-algebras satisfying some algebraic properties, like the Auslander-Gorenstein property, the condition to be Cohen-Macaulay and the coincidence of injective and Gelfand-Kirillov dimensions. This local duality is a non-commutative version of local duality on commutative Gorenstein rings. In the known cases of enveloping algebras of finite-dimensional solvable Lie algebras and some of their extensions the codimension of cofinite prime ideals was \(1\). In the first part of the paper the authors develop the theory and obtain a characterization of local dualities. In the second one they introduce some examples of non-commutative algebras having a local duality. Among these examples, extra attention is paid to the quantum plane, because it provides examples of \(K\)-algebras in which the codimension of the cofinite prime ideals is greater than one.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 16E65
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16B50
Mathematics Subject Classification ID: 16P90
Mathematics Subject Classification ID: 16S90
Mathematics Subject Classification ID: 16W35
zbMATH DE Number: 1496429
zbMATH Keywords: Gorenstein rings
zbMATH Keywords: local dualities
zbMATH Keywords: Gröbner bases
zbMATH Keywords: modules
zbMATH Keywords: Gelfand-Kirillov dimension
zbMATH Keywords: injective dimension
author: P. Jara
author: Jorge Jódar
MaRDI profile type: Publication
full work available at URL: aima.1998.1878
OpenAlex ID: W1970646996
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DOI: 10.1006/AIMA.1998.1878
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description: scientific article; zbMATH DE number 1496429