Deformations of Lie algebras
type: Item
instance of: scholarly article
title: Deformations of Lie algebras
zbMATH Open document ID: 0799.17007
author: Joyce O'Halloran
author: Fritz Grunewald
published in: Journal of Algebra
publication date: 1994-11-22T00:00:00Z
review text: The paper is devoted to the study of the deformations of nilpotent Lie algebras over an algebraically closed field of characteristic 0. After some remarks giving reasons for it the authors consider the deformations of the type \(a\circ b= [a,b]+ t\psi(a,b)\), where \(a\circ b\) is a new multiplication on Lie algebra \(L\) and \(\psi\in Z^ 2(L,L)\). The main result states that nilpotent Lie algebra \(L\) has a non-trivial deformation if some codimension 1 ideal \(K\) of \(L\) has a nonsingular derivation. The proof is based on Dixmier's construction of 2-cochains in \(C^ 2(L,L)\) from 1-cochains in \(C^ 1(K,K)\). After that the authors consider some classes of nilpotent Lie algebras in which such an ideal may be constructed. In the paper Dixmier's construction is applied to obtain non-trivial deformations for some other Lie algebras as well.
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 17B56
zbMATH DE Number: 554205
zbMATH Keywords: deformations
zbMATH Keywords: nilpotent Lie algebras
reviewed by: Michael Kuznetsov
MaRDI profile type: Publication
full work available at URL: jabr.1993.1250
OpenAlex ID: W2076315775
Wikidata QID: Q115396273
DOI: 10.1006/JABR.1993.1250
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description: scientific article; zbMATH DE number 554205