Lie σ-derivations of triangular algebras

Let be a triangular algebra and σ be an automorphism of . We consider the problem of describing the form of Lie σ-derivations of . In particular, we give sufficient conditions that every Lie σ-derivation d of is the sum , where Δ is a σ-derivation of and γ is a linear mapping from to its σ-centre th...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 70; no. 15; pp. 2966 - 2983
Main Author Benkovič, Dominik
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 13.10.2022
Taylor & Francis Ltd
Subjects
Algebra
Automorphisms
Derivation
Lie σ-derivation
nest algebra
triangular algebra
σ-centre map
σ-derivation
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Summary:Let be a triangular algebra and σ be an automorphism of . We consider the problem of describing the form of Lie σ-derivations of . In particular, we give sufficient conditions that every Lie σ-derivation d of is the sum , where Δ is a σ-derivation of and γ is a linear mapping from to its σ-centre that vanishes on . As an application, Lie σ-derivations of (block) upper triangular matrix algebras and nest algebras are determined.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2020.1820431