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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| Дата: | 2023 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2023
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1895 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543297613332480 |
|---|---|
| author | Shermatova, Z. Khudoyberdiyev, A. |
| author_facet | Shermatova, Z. Khudoyberdiyev, A. |
| author_sort | Shermatova, Z. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2023-03-06T16:39:17Z |
| description | 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. |
| first_indexed | 2025-12-02T15:25:55Z |
| format | Article |
| id | admjournalluguniveduua-article-1895 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:25:55Z |
| publishDate | 2023 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-18952023-03-06T16:39:17Z On special subalgebras of derivations of Leibniz algebras Shermatova, Z. Khudoyberdiyev, A. Leibniz algebra, radical, nilradical, inner derivation, central derivation 17A32, 17A36, 17B30, 17B56 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. Lugansk National Taras Shevchenko University 2023-03-06 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1895 10.12958/adm1895 Algebra and Discrete Mathematics; Vol 34, No 2 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1895/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1895/939 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1895/979 Copyright (c) 2023 Algebra and Discrete Mathematics |
| spellingShingle | Leibniz algebra radical nilradical inner derivation central derivation 17A32 17A36 17B30 17B56 Shermatova, Z. Khudoyberdiyev, A. On special subalgebras of derivations of Leibniz algebras |
| title | On special subalgebras of derivations of Leibniz algebras |
| title_full | On special subalgebras of derivations of Leibniz algebras |
| title_fullStr | On special subalgebras of derivations of Leibniz algebras |
| title_full_unstemmed | On special subalgebras of derivations of Leibniz algebras |
| title_short | On special subalgebras of derivations of Leibniz algebras |
| title_sort | on special subalgebras of derivations of leibniz algebras |
| topic | Leibniz algebra radical nilradical inner derivation central derivation 17A32 17A36 17B30 17B56 |
| topic_facet | Leibniz algebra radical nilradical inner derivation central derivation 17A32 17A36 17B30 17B56 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1895 |
| work_keys_str_mv | AT shermatovaz onspecialsubalgebrasofderivationsofleibnizalgebras AT khudoyberdiyeva onspecialsubalgebrasofderivationsofleibnizalgebras |