Local and 2-local $\frac{1}{2}$-derivations on finite-dimensional Lie algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916126360862720 |
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| author | Khudoyberdiyev, Abror Yusupov, Bakhtiyor |
| author_facet | Khudoyberdiyev, Abror Yusupov, Bakhtiyor |
| contents | In this work, we introduce the notion of local and $2$-local $δ$-derivations and describe local and $2$-local $\frac{1}{2}$-derivation of finite-dimensional solvable Lie algebras with filiform, Heisenberg, and abelian nilradicals. Moreover, we describe the local $\frac{1}{2}$-derivation of oscillator Lie algebras, Schr{ö}dinger algebras, and Lie algebra with a three-dimensional simple part, whose radical is an irreducible module. We prove that an algebra with only trivial $\frac{1}{2}$-derivation does not admit local and $2$-local $\frac{1}{2}$-derivation, which is not $\frac{1}{2}$-derivation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09818 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local and 2-local $\frac{1}{2}$-derivations on finite-dimensional Lie algebras Khudoyberdiyev, Abror Yusupov, Bakhtiyor Rings and Algebras In this work, we introduce the notion of local and $2$-local $δ$-derivations and describe local and $2$-local $\frac{1}{2}$-derivation of finite-dimensional solvable Lie algebras with filiform, Heisenberg, and abelian nilradicals. Moreover, we describe the local $\frac{1}{2}$-derivation of oscillator Lie algebras, Schr{ö}dinger algebras, and Lie algebra with a three-dimensional simple part, whose radical is an irreducible module. We prove that an algebra with only trivial $\frac{1}{2}$-derivation does not admit local and $2$-local $\frac{1}{2}$-derivation, which is not $\frac{1}{2}$-derivation. |
| title | Local and 2-local $\frac{1}{2}$-derivations on finite-dimensional Lie algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2402.09818 |