$δ$-Leibniz algebras and related $δ$-type algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912925448404992 |
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| author | Adashev, Jobir Kaygorodov, Ivan |
| author_facet | Adashev, Jobir Kaygorodov, Ivan |
| contents | This paper introduces and investigates the structure of $δ$-Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar $δ$. The authors define $δ$-Lie algebras, $δ$-Lie dialgebras, and $δ$-Zinbiel algebras via a standard procedure and study their fundamental properties. Furthermore, the research describes symmetric $δ$-Leibniz algebras and algebras of $δ$-biderivation type, establishing their connections with nilalgebras. Finally, these results provide a unified framework for understanding various classes of non-associative algebras through the lens of the $δ$ parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21210 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $δ$-Leibniz algebras and related $δ$-type algebras Adashev, Jobir Kaygorodov, Ivan Rings and Algebras This paper introduces and investigates the structure of $δ$-Leibniz algebras, which serve as a parametric generalization of classical Leibniz algebras defined by a scalar $δ$. The authors define $δ$-Lie algebras, $δ$-Lie dialgebras, and $δ$-Zinbiel algebras via a standard procedure and study their fundamental properties. Furthermore, the research describes symmetric $δ$-Leibniz algebras and algebras of $δ$-biderivation type, establishing their connections with nilalgebras. Finally, these results provide a unified framework for understanding various classes of non-associative algebras through the lens of the $δ$ parameter. |
| title | $δ$-Leibniz algebras and related $δ$-type algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2602.21210 |