Delta ideals of Lie color algebras
type: Item
instance of: scholarly article
title: Delta ideals of Lie color algebras
zbMATH Open document ID: 0837.17006
author: Jeffrey Bergen
author: D. S. Passman
published in: Journal of Algebra
publication date: 1996-05-21T00:00:00Z
review text: Let \(L\) be a Lie color algebra, possibly restricted, over a field \(K\) and graded by a finite abelian group \(G\). The authors show that if \(L\) has no nonzero elements with centralizers of countable codimension, then its enveloping algebra \(U(L)\) is ``symmetrically closed'' in the sense that it coincides with its symmetric Martindale quotient ring [see the second author, J. Algebra 105, 207-235 (1987; Zbl 0605.16003) for the definition]. They also show that the Lie color ideal \(\Delta(L)\) consisting of the elements whose centralizers have finite codimension has derived subalgebra sitting inside the join \(\Delta_L\) of all the finite-dimensional Lie color ideals of \(L\). These results are new even for ordinary or super Lie algebras.
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 17A70
zbMATH DE Number: 827375
zbMATH Keywords: delta ideals
zbMATH Keywords: symmetric ring of quotients
zbMATH Keywords: enveloping algebra
zbMATH Keywords: Lie color algebra
reviewed by: William M. McGovern
MaRDI profile type: Publication
full work available at URL: jabr.1995.1327
OpenAlex ID: W1976009536
Wikidata QID: Q115396146
DOI: 10.1006/JABR.1995.1327
description: scientific article; zbMATH DE number 827375