Lie triple derivations of unital algebras with idempotents

Let be a unital algebra with a nontrivial idempotent over a unital commutative ring . We show that under suitable assumptions, every Lie triple derivation on is of the form , where is a derivation of , is a singular Jordan derivation of and is a linear mapping from to its centre that vanishes on . A...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 63; no. 1; pp. 141 - 165
Main Author Benkovic, Dominik
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2015
Taylor & Francis Ltd
Subjects
Algebra
Derivation
Jordan derivation
Lie derivation
Lie triple derivation
Mapping
Mathematical analysis
Matrix algebra
Rings (mathematics)
triangular algebra
unital algebra
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Summary:Let be a unital algebra with a nontrivial idempotent over a unital commutative ring . We show that under suitable assumptions, every Lie triple derivation on is of the form , where is a derivation of , is a singular Jordan derivation of and is a linear mapping from to its centre that vanishes on . As an application, we characterize Lie triple derivations and Lie derivations on triangular algebras and on matrix algebras.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2013.851200