\((\mathcal{T}_{\textsf {Lie}})\)-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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| Date: | 2024 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2024
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2049 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Summary: | 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. |
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