Leibniz algebras with absolute maximal Lie subalgebras
A Lie subalgebra of a given Leibniz algebra is said to be an absolute maximal Lie subalgebra if it has codimension one. In this paper, we study some properties of non-Lie Leibniz algebras containing absolute maximal Lie subalgebras. When the dimension and codimension of their Lie-center are greater...
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| Дата: | 2020 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2020
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1165 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543049698508800 |
|---|---|
| author | Biyogmam, G. R. Tcheka, C. |
| author_facet | Biyogmam, G. R. Tcheka, C. |
| author_sort | Biyogmam, G. R. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-05-14T18:27:22Z |
| description | A Lie subalgebra of a given Leibniz algebra is said to be an absolute maximal Lie subalgebra if it has codimension one. In this paper, we study some properties of non-Lie Leibniz algebras containing absolute maximal Lie subalgebras. When the dimension and codimension of their Lie-center are greater than two, we refer to these Leibniz algebras as \(s\)-Leibniz algebras (strong Leibniz algebras). We provide a classification of nilpotent Leibniz \(s\)-algebras of dimension up to five. |
| first_indexed | 2025-12-02T15:49:57Z |
| format | Article |
| id | admjournalluguniveduua-article-1165 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:49:57Z |
| publishDate | 2020 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-11652020-05-14T18:27:22Z Leibniz algebras with absolute maximal Lie subalgebras Biyogmam, G. R. Tcheka, C. Leibniz algebras, \(s\)-Leibniz algebras, Lie-center 17A32, 17B55, 18B99 A Lie subalgebra of a given Leibniz algebra is said to be an absolute maximal Lie subalgebra if it has codimension one. In this paper, we study some properties of non-Lie Leibniz algebras containing absolute maximal Lie subalgebras. When the dimension and codimension of their Lie-center are greater than two, we refer to these Leibniz algebras as \(s\)-Leibniz algebras (strong Leibniz algebras). We provide a classification of nilpotent Leibniz \(s\)-algebras of dimension up to five. Lugansk National Taras Shevchenko University 2020-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1165 10.12958/adm1165 Algebra and Discrete Mathematics; Vol 29, No 1 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1165/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1165/475 Copyright (c) 2020 Algebra and Discrete Mathematics |
| spellingShingle | Leibniz algebras \(s\)-Leibniz algebras Lie-center 17A32 17B55 18B99 Biyogmam, G. R. Tcheka, C. Leibniz algebras with absolute maximal Lie subalgebras |
| title | Leibniz algebras with absolute maximal Lie subalgebras |
| title_full | Leibniz algebras with absolute maximal Lie subalgebras |
| title_fullStr | Leibniz algebras with absolute maximal Lie subalgebras |
| title_full_unstemmed | Leibniz algebras with absolute maximal Lie subalgebras |
| title_short | Leibniz algebras with absolute maximal Lie subalgebras |
| title_sort | leibniz algebras with absolute maximal lie subalgebras |
| topic | Leibniz algebras \(s\)-Leibniz algebras Lie-center 17A32 17B55 18B99 |
| topic_facet | Leibniz algebras \(s\)-Leibniz algebras Lie-center 17A32 17B55 18B99 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1165 |
| work_keys_str_mv | AT biyogmamgr leibnizalgebraswithabsolutemaximalliesubalgebras AT tchekac leibnizalgebraswithabsolutemaximalliesubalgebras |