\((\mathcal{T}_{\textsf {Lie}})\)-Leibniz algebras and related properties
In this paper, we study properties of Leibniz algebras of class \(\mathcal{T}_{\textsf {Lie}}\), a subclass of both the class \(\mathfrak{D}_{\textsf {Lie}}\) and the class of \({\textsf {Lie}}\)-stem Leibniz algebras. We determine necessary and sufficient conditions under which a non-Lie Leibniz al...
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| Дата: | 2024 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2024
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2049 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-20492024-02-14T18:40:04Z \((\mathcal{T}_{\textsf {Lie}})\)-Leibniz algebras and related properties Tcheka, C. Kamgam Dayo, A. Biyogmam, G. R. Leibniz algebras, \(\mathcal{T}_{Lie}\)-Leibniz algebras, \({\textsf {Lie}}\)-stem Leibniz algebras, \({\textsf {Lie}}\)-central derivations 17A32; 17A36; 17B40 In this paper, we study properties of Leibniz algebras of class \(\mathcal{T}_{\textsf {Lie}}\), a subclass of both the class \(\mathfrak{D}_{\textsf {Lie}}\) and the class of \({\textsf {Lie}}\)-stem Leibniz algebras. We determine necessary and sufficient conditions under which a non-Lie Leibniz algebra is of class \(\mathcal{T}_{\textsf {Lie}}\) and study their relationship with pseudo-abelian Leibniz algebras. We also show that Leibniz algebras of class \(\mathcal{T}_{\textsf {Lie}}\) have semi-simple central \({\textsf {Lie}}\)-derivations. Lugansk National Taras Shevchenko University Calvin Tcheka, University of Dschang, Département of Mathematics and computer sciences Ariane Kamgam Dayo, University of Dschang, Département of Mathematics and computer sciences Guy Roger Biyogmam, Georgia Collège and State University, Département of 2024-02-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2049 10.12958/adm2049 Algebra and Discrete Mathematics; Vol 36, No 2 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2049/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2049/1034 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2049/1035 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2049/1139 Copyright (c) 2024 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Leibniz algebras \(\mathcal{T}_{Lie}\)-Leibniz algebras \({\textsf {Lie}}\)-stem Leibniz algebras \({\textsf {Lie}}\)-central derivations 17A32; 17A36; 17B40 |
| spellingShingle |
Leibniz algebras \(\mathcal{T}_{Lie}\)-Leibniz algebras \({\textsf {Lie}}\)-stem Leibniz algebras \({\textsf {Lie}}\)-central derivations 17A32; 17A36; 17B40 Tcheka, C. Kamgam Dayo, A. Biyogmam, G. R. \((\mathcal{T}_{\textsf {Lie}})\)-Leibniz algebras and related properties |
| topic_facet |
Leibniz algebras \(\mathcal{T}_{Lie}\)-Leibniz algebras \({\textsf {Lie}}\)-stem Leibniz algebras \({\textsf {Lie}}\)-central derivations 17A32; 17A36; 17B40 |
| format |
Article |
| author |
Tcheka, C. Kamgam Dayo, A. Biyogmam, G. R. |
| author_facet |
Tcheka, C. Kamgam Dayo, A. Biyogmam, G. R. |
| author_sort |
Tcheka, C. |
| title |
\((\mathcal{T}_{\textsf {Lie}})\)-Leibniz algebras and related properties |
| title_short |
\((\mathcal{T}_{\textsf {Lie}})\)-Leibniz algebras and related properties |
| title_full |
\((\mathcal{T}_{\textsf {Lie}})\)-Leibniz algebras and related properties |
| title_fullStr |
\((\mathcal{T}_{\textsf {Lie}})\)-Leibniz algebras and related properties |
| title_full_unstemmed |
\((\mathcal{T}_{\textsf {Lie}})\)-Leibniz algebras and related properties |
| title_sort |
\((\mathcal{t}_{\textsf {lie}})\)-leibniz algebras and related properties |
| description |
In this paper, we study properties of Leibniz algebras of class \(\mathcal{T}_{\textsf {Lie}}\), a subclass of both the class \(\mathfrak{D}_{\textsf {Lie}}\) and the class of \({\textsf {Lie}}\)-stem Leibniz algebras. We determine necessary and sufficient conditions under which a non-Lie Leibniz algebra is of class \(\mathcal{T}_{\textsf {Lie}}\) and study their relationship with pseudo-abelian Leibniz algebras. We also show that Leibniz algebras of class \(\mathcal{T}_{\textsf {Lie}}\) have semi-simple central \({\textsf {Lie}}\)-derivations. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2024 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2049 |
| work_keys_str_mv |
AT tchekac mathcalttextsflieleibnizalgebrasandrelatedproperties AT kamgamdayoa mathcalttextsflieleibnizalgebrasandrelatedproperties AT biyogmamgr mathcalttextsflieleibnizalgebrasandrelatedproperties |
| first_indexed |
2024-04-12T06:25:42Z |
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2024-04-12T06:25:42Z |
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1796109193584836608 |