Lie centrally metabelian group rings in characteristic 3
type: Item
instance of: scholarly article
title: Lie centrally metabelian group rings in characteristic 3
zbMATH Open document ID: 0845.16020
published in: Journal of Algebra
publication date: 1996-06-03T00:00:00Z
review text: Let \(L\) be a Lie algebra over a field \(F\), \(L'=[L,L]\) and \(L''=(L')'\). The Lie algebra \(L\) is called centrally metabelian if \([L'',L]=0\). Let \(A\) be an associative unitary algebra over a field \(F\) and let \({\mathfrak L} (A)\) be the Lie algebra which has the same underlying vector space as \(A\) and which satisfies \([a,b]=ab-ba\) for \(a, b\in A\). The algebra \(A\) is called Lie centrally metabelian if \({\mathfrak L}(A)\) is centrally metabelian. Let \(FG\) be the group algebra of a group \(G\) over a field \(F\) of characteristic 3. A necessary and sufficient condition for \(FG\) to be centrally metabelian is given. It is the main result of the paper.
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 17B60
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 20C07
zbMATH DE Number: 869803
zbMATH Keywords: centrally metabelian Lie algebras
zbMATH Keywords: group algebras
author: Burkhard Külshammer
author: Rajendra Kumar Sharma
reviewed by: Todor Mollov
MaRDI profile type: Publication
full work available at URL: jabr.1996.0055
OpenAlex ID: W2083525544
Wikidata QID: Q115396115
DOI: 10.1006/JABR.1996.0055
description: scientific article; zbMATH DE number 869803