Uniqueness of Joseph ideal
type: Item
instance of: scholarly article
title: Uniqueness of Joseph ideal
zbMATH Open document ID: 1112.17014
author: Gordan Savin
author: Wee Teck Gan
published in: Mathematical Research Letters
publication date: 2005-04-05T00:00:00Z
review text: Let \(\mathfrak g\) be a simple complex Lie algebra. For any ideal \(\mathcal J\) of the universal enveloping algebra \(U({\mathfrak g})\) of \(\mathfrak g\) one associates an ideal gr\(({\mathcal J})\) in the symmetric algebra \(U({\mathfrak g})\) of \(\mathfrak g\). If \(\mathcal J\) is primitive, then the associated variety Ass\(({\mathcal J})\) (i.e. the zero set of gr\(({\mathcal J})\) in \(\mathfrak g\)) is contained in the nilpotent cone of \(\mathfrak g\). In 1976 Joseph constructed a completely prime two-sided primitive ideal of \(U({\mathfrak g})\) whose associated variety is the closure of the minimal orbit \({\mathbf O}_{min}\) of \(\mathfrak g\). If \(\mathfrak g\) is not of type A, then the Joseph ideal is unique with this property. In the paper under review the authors provide a new simple proof of the uniqueness of the Joseph ideal which is different from the original proof of Joseph.
reviewed by: Vesselin Drensky
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 16S30
zbMATH DE Number: 2152362
zbMATH Keywords: simple Lie algebras
zbMATH Keywords: universal enveloping algebras
zbMATH Keywords: Joseph ideal
zbMATH Keywords: minimal nilpotent orbit
MaRDI profile type: Publication
full work available at URL: mrl.2004.v11.n5.a4
OpenAlex ID: W2015112562
DOI: 10.4310/MRL.2004.V11.N5.A4
description: scientific article; zbMATH DE number 2152362