On special subalgebras of derivations of Leibniz algebras
Our aim in this work is to study the central derivations of Leibniz algebras and investigate the properties of Leibniz algebras by comparing the set of central derivations with the inner derivations. We prove that, the set of all central derivations of a Leibniz algebra with non-trivial center coinc...
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| Date: | 2023 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2023
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1895 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | Our aim in this work is to study the central derivations of Leibniz algebras and investigate the properties of Leibniz algebras by comparing the set of central derivations with the inner derivations. We prove that, the set of all central derivations of a Leibniz algebra with non-trivial center coincide with the set of all inner derivations if and only if the Leibniz algebra is metabelian. In addition, we will show, by examples, that some statements hold for arbitrary Lie algebras, but does not hold for some Leibniz algebras. |
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