Generalized Lie n-derivations of triangular algebras

Let be a triangular algebra. We show that under suitable assumptions every generalized Lie n-derivation associated with a linear map is of the form where and Δ is a Lie n-derivation of We solve this problem using commuting and centralizing maps. We also prove that under certain mild conditions any c...

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Bibliographic Details
Published inCommunications in algebra Vol. 47; no. 12; pp. 5294 - 5302
Main Author Benkovič, Dominik
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.12.2019
Taylor & Francis Ltd
Subjects
Algebra
Derivation
generalized Lie n-derivation
Lie n-derivation
triangular algebra
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Summary:Let be a triangular algebra. We show that under suitable assumptions every generalized Lie n-derivation associated with a linear map is of the form where and Δ is a Lie n-derivation of We solve this problem using commuting and centralizing maps. We also prove that under certain mild conditions any centralizing map on a triangular algebra is commuting. As an application, we give a description of generalized Lie n-derivations on classical examples of triangular algebras: upper triangular matrix algebras and nest algebras.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2019.1617875