Multiplicative Lie \(n\)-derivations of generalized matrix algebras.
type: Item
instance of: scholarly article
title: Multiplicative Lie \(n\)-derivations of generalized matrix algebras.
zbMATH Open document ID: 1272.16039
author: Yao Wang
author: Yu Wang
published in: Linear Algebra and its Applications
publication date: 2013-02-22T00:00:00Z
review text: A nonlinear Lie \(n\)-derivation of an algebra \(A\) is a (not necessarily linear) map of \(A\) that acts as a derivation on the polynomial \([[\cdots[x_1,x_2],\dots],x_n]\). The main result states that a nonlinear Lie \(n\)-derivation of a generalized matrix algebra is, under certain technical assumptions, the sum of an (additive) derivation and a map with the range in the center that vanishes on commutators. As a corollary it is shown that if \(A\) is a full matrix algebra \(M_n(B)\), where \(B\) is a unital algebra, then this holds under rather mild assumptions. This was conjectured by \textit{D. Benkovič} and \textit{D. Eremita} [Linear Algebra Appl. 436, No. 11, 4223-4240 (2012; Zbl 1247.16040)].
Mathematics Subject Classification ID: 16W25
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 15A78
zbMATH DE Number: 6138439
zbMATH Keywords: nonlinear Lie \(n\)-derivations
zbMATH Keywords: additive derivations
zbMATH Keywords: generalized matrix algebras
zbMATH Keywords: full matrix algebras
reviewed by: Matej Brešar
MaRDI profile type: Publication
full work available at URL: j.laa.2012.10.052
OpenAlex ID: W2023589254
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Wikidata QID: Q115344622
DOI: 10.1016/J.LAA.2012.10.052
description: scientific article; zbMATH DE number 6138439