Some inequalities for the dimension of the \(c\)-nilpotent multiplier of Lie algebras
type: Item
instance of: scholarly article
title: Some inequalities for the dimension of the \(c\)-nilpotent multiplier of Lie algebras
zbMATH Open document ID: 1229.17010
author: Ali Reza Salemkar
author: Behrouz Edalatzadeh
author: Mehdi Araskhan
published in: Journal of Algebra
publication date: 2009-10-13T00:00:00Z
review text: Corresponding to the Baer invariant of a group with respect to the variety of nilpotent groups, the authors define the c-nilpotent multiplier for a Lie algebra, \(L\). When \(c=1\), one obtains the Schur multiplier of \(L\). The \(c\)-nilpotent multiplier is abelian, hence is characterized by it's dimension, and is independent of the free presentation of \(L\) that is used in it's definition. Bounds on this dimension are obtained. The related concept of c-cover of \(L\) is also studied. Unlike the case when \(c=1\), c-covers may not exist. Here one only needs to take an abelian Lie algebra of dimension at least 2 and \(c\) to be at least 2. However, for \(c\)-perfect algebras, \(c\)-covers are shown to exist.
reviewed by: Ernest L. Stitzinger
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 5614721
zbMATH Keywords: Schur multiplier
zbMATH Keywords: cover
zbMATH Keywords: nilpotent Lie algebra
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2009.05.036
OpenAlex ID: W2087740908
Wikidata QID: Q115351298
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DOI: 10.1016/J.JALGEBRA.2009.05.036
description: scientific article; zbMATH DE number 5614721