The multiplier and the cover of direct sums of Lie algebras
type: Item
instance of: scholarly article
zbMATH Open document ID: 1272.17018
DOI: 10.1142/S179355711250026X
author: Ali Reza Salemkar
author: Behrouz Edalatzadeh
published in: Asian-European Journal of Mathematics
publication date: 2012-10-16T00:00:00Z
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 6094202
zbMATH Keywords: Schur multiplier
zbMATH Keywords: cover
MaRDI profile type: Publication
cites work: On covers of lie algebras
cites work: On characterizing nilpotent lie algebras by their multipliers
cites work: Nonabelian exterior products of Lie algebras and an exact sequence in the homology of Lie algebras
cites work: Some Properties of the Schur Multiplier and Covers of Lie Algebras
cites work: SOME PROPERTIES ON ISOCLINISM OF LIE ALGEBRAS AND COVERS
cites work: Some inequalities for the dimension of the \(c\)-nilpotent multiplier of Lie algebras
cites work: On Covers of Perfect Lie Algebras
full work available at URL: s179355711250026x
OpenAlex ID: W2144519908
title: The multiplier and the cover of direct sums of Lie algebras
review text: The authors obtain an analog to the group theory result of \textit{C. Miller} [Proc. Am. Math. Soc. 3, 588--595 (1952; Zbl 0047.25703)] when they show the the Schur multiplier of the direct sum of two Lie algebras is the direct sum of the multipliers of the factors and the tensor product of the factors. In the finite dimensional case, the result was shown by \textit{P. Batten, K. Moneyhun} and the reviewer [Commun. Algebra 24, No. 14, 4319--4330 (1996; Zbl 0893.17008)]. They also obtain that the cover for the direct sum of two Lie algebras is the direct sum of the covers of the factors and the tensor product of the covers of the factors.
reviewed by: Ernest L. Stitzinger
description: scientific article; zbMATH DE number 6094202