Generalized derivations of $ω$-Lie algebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912328285421568 |
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| author | Chen, Yin Ren, Shan Shan, Jiawen Zhang, Runxuan |
| author_facet | Chen, Yin Ren, Shan Shan, Jiawen Zhang, Runxuan |
| contents | This article explores the structure theory of compatible generalized derivations of finite-dimensional $ω$-Lie algebras over a field $\mathbb{K}$. We prove that any compatible quasiderivation of an $ω$-Lie algebra can be embedded as a compatible derivation into a larger $ω$-Lie algebra, refining the general result established by Leger and Luks in 2000 for finite-dimensional nonassociative algebras. We also provide an approach to explicitly compute (compatible) generalized derivations and quasiderivations for all $3$-dimensional non-Lie complex $ω$-Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized derivations of $ω$-Lie algebras Chen, Yin Ren, Shan Shan, Jiawen Zhang, Runxuan Rings and Algebras 17B40 This article explores the structure theory of compatible generalized derivations of finite-dimensional $ω$-Lie algebras over a field $\mathbb{K}$. We prove that any compatible quasiderivation of an $ω$-Lie algebra can be embedded as a compatible derivation into a larger $ω$-Lie algebra, refining the general result established by Leger and Luks in 2000 for finite-dimensional nonassociative algebras. We also provide an approach to explicitly compute (compatible) generalized derivations and quasiderivations for all $3$-dimensional non-Lie complex $ω$-Lie algebras. |
| title | Generalized derivations of $ω$-Lie algebras |
| topic | Rings and Algebras 17B40 |
| url | https://arxiv.org/abs/2503.11595 |