Localization in rings equipped with an action of a solvable Lie algebra
type: Item
instance of: scholarly article
title: Localization in rings equipped with an action of a solvable Lie algebra
zbMATH Open document ID: 0892.16015
author: T. Guédénon
published in: Journal of Algebra
publication date: 1998-01-26T00:00:00Z
review text: In [Compos. Math. 53, 347-367 (1984; Zbl 0561.16003)], the reviewer showed that the clique of a prime ideal of the enveloping algebra of a finite dimensional complex solvable Lie algebra \(\mathfrak g\) is localizable, and gave detailed results on the structure of the localized ring. Let \(R\) be a commutative Noetherian \(\mathbb{C}\)-algebra on which \(\mathfrak g\) acts as derivations, and set \(A=R\# U({\mathfrak g})\). Localizability of the cliques of \(A\) was proved by \textit{K. R. Goodearl} [J. Algebra 132, No. 1, 243-262 (1990; Zbl 0712.16017)]. The purpose of the article under review is to extend some of the structural results proved by the reviewer for the localizations of \(U({\mathfrak g})\) to the more general setting of \(R\# U({\mathfrak g})\). In particular, for the Ore set \(\mathcal T\) determined by a clique of \(A\), some sufficient conditions are given for the primitive ideals of \(A_{\mathcal T}\) to be generated by regular normalizing sequences.
Mathematics Subject Classification ID: 16S32
Mathematics Subject Classification ID: 16S30
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 1104104
zbMATH Keywords: localizability
zbMATH Keywords: cliques of prime ideals
zbMATH Keywords: enveloping algebras
zbMATH Keywords: finite dimensional complex solvable Lie algebras
zbMATH Keywords: localizations
zbMATH Keywords: Ore sets
zbMATH Keywords: primitive ideals
zbMATH Keywords: regular normalizing sequences
reviewed by: Kenneth A. Brown
MaRDI profile type: Publication
full work available at URL: jabr.1997.7074
OpenAlex ID: W2007321295
Wikidata QID: Q115395981
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DOI: 10.1006/JABR.1997.7074
description: scientific article; zbMATH DE number 1104104